Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C491⋊C16 |
| unambiguous semidirect product | (C2×C491)⋊C16 |
| derived, Sylow | C491 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D491 |
| commutator, hypocenter | C491 | C2×C16 |
| Frattini | C8 | C2×D491 |
| Fitting | C2×C8×C491 | C2 |
| socle, prime radical | C22×C491 | C8 |
| cosocle | C8×C491 | C22 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C2×C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
3952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic491, C4×C491⋊C16, #44536500, … |
| maximal normal subgroup of | C16×Dic491, C4×C491⋊C16, #44536500, … |
| maximal quotient of | C4×C491⋊C16, C22⋊(C491⋊C16), C4⋊(C491⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 84);