Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×C83⋊C8 |
| Sylow | C83 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×C83⋊C8, #35294948, #35294952, … |
| maximal normal subgroup of | #99×C83⋊C8, #35294948, #35294952, … |
| maximal quotient of | C2×D8×C83⋊C8, C2×SD16×C83⋊C8, C2×Q16×C83⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13183);