Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14581792 |
| Sylow | C83 ⋊ C22×C4⋊Q8 |
1624 conjugacy classes of subgroups.
2680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295890, #35295892, #35295899, … |
| maximal normal subgroup of | #35295890, #35295892, #35295899, … |
| maximal quotient of | C22×#19127571, C22×#19127599, C22×#19127607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17786);