Looks like a compound of 2 sophips, and indeed all elements coincide by pairs.

Incidence matrix according to Dynkin symbol

x x5o5/2o5x

. . .   . .    | 2880 |    1    10 |   10   10   10 |   10   10   2   10 |   2   10 1
---------------+------+------------+----------------+--------------------+-----------
x . .   . .    |    2 | 1440     * |   10    0    0 |   10   10   0    0 |   2   10 0
. x .   . .  & |    2 |    * 14400 |    1    2    2 |    2    2   1    3 |   1    3 1
---------------+------+------------+----------------+--------------------+-----------
x x .   . .  & |    4 |    2     2 | 7200    *    * |    2    2   0    0 |   1    3 0
. x5o   . .  & |    5 |    0     5 |    * 5760    * |    1    0   1    1 |   1    1 1
. x .   . x    |    4 |    0     4 |    *    * 7200 |    0    1   0    2 |   0    2 1
---------------+------+------------+----------------+--------------------+-----------
x x5o   . .  & ♦   10 |    5    10 |    5    2    0 | 2880    *   *    * |   1    1 0
x x .   . x    ♦    8 |    4     8 |    4    0    2 |    * 3600   *    * |   0    2 0
. x5o5/2o .  & ♦   12 |    0    30 |    0   12    0 |    *    * 480    * |   1    0 1
. x5o   . x  & ♦   10 |    0    15 |    0    2    5 |    *    *   * 2880 |   0    1 1
---------------+------+------------+----------------+--------------------+-----------
x x5o5/2o .  & ♦   24 |   12    60 |   30   24    0 |   12    0   2    0 | 240    * *
x x5o   . x  & ♦   20 |   10    30 |   15    4   10 |    2    5   0    2 |   * 1440 *
. x5o5/2o5x    ♦ 1440 |    0  7200 |    0 2880 3600 |    0    0 240 1440 |   *    * 2

snubbed forms: β2β5o5/2o5x