Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×C8×Dic166 |
| Sylow | C83 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14581710, #35294978, C8×#14581717, … |
| maximal normal subgroup of | C8×#14581710, #35294978, C8×#14581717, … |
| maximal quotient of | C2×C8×C4⋊Dic83, C2×C8×Dic83⋊C4, C4×C8×Dic166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13431);