Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×Dic491 |
| unambiguous semidirect product | (C2×C491)⋊C42 |
| derived, Sylow | C491 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D491 |
| commutator, hypocenter | C491 | C2×C42 |
| Frattini | C22 | C22×D491 |
| Fitting | C22×C4×C491 | C2 |
| socle, prime radical | C23×C491 | C22 |
| cosocle | C22×C491 | C23 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C22×C4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
3952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536479, #44536484, #44536486, … |
| maximal normal subgroup of | #44536479, #44536484, #44536486, … |
| maximal quotient of | C42×Dic491, C2×C491⋊#95, #44536571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 95);