Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19128298 |
| Fitting | C22×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#539 |
1144 conjugacy classes of subgroups.
1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296225, #35296229, #35370433, … |
| maximal normal subgroup of | #35296225, #35296229, #35370433, … |
| maximal quotient of | C2×#24910066, C2×#24910097, C2×#24910132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17861);