Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D491 |
| unambiguous semidirect product | C491⋊C25 |
| unambiguous semidirect product | (C2×C491)⋊C24 |
| Fitting, socle | C24×C491 ⋊ C2 |
| derived, Sylow | C491 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D491 |
| commutator, cosocle, hypocenter | C491 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C491 | C2 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
3952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536580, C2×C22⋊C4×D491, C22×(C2×D491)⋊C4, … |
| maximal normal subgroup of | #44536580, C2×C22⋊C4×D491, C22×(C2×D491)⋊C4, … |
| maximal quotient of | C23×C4×D491, C24×Dic491, C22×D4×D491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 195);