Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C23×#13050574 |
| Sylow | C83 ⋊ C23×M16 |
1720 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309631, #35309633, #35309639, … |
| maximal normal subgroup of | #35309631, #35309633, #35309639, … |
| maximal quotient of | C23×#14581703, C22×C4×#13050574, C23×C22⋊(C83⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19212);