Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#117×D83 |
| Fitting | C2×#117×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×#117 |
1880 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309634, #35309692, #35309712, … |
| maximal normal subgroup of | #35309634, #35309692, #35309712, … |
| maximal quotient of | C2×#376×D83, C2×C4×C22⋊C4×D83, C2×C4×C4⋊C4×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17672);