Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×D491 |
| Fitting | C16×C491 ⋊ C2 |
| derived, Sylow | C491 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | D491 |
| commutator, hypocenter | C491 | C2×C16 |
| Frattini | C8 | C2×D491 |
| Fitting | C16×C491 | C2 |
| socle | C2×C491 | C2×C8 |
| prime radical | C2×D491 | C8 |
| cosocle | C8×C491 | C22 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C16 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
3952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D491, #44536558, C2×C16×D491, … |
| maximal normal subgroup of | C32×D491, #44536558, C2×C16×D491, … |
| maximal quotient of | C16×Dic491, (C2×D491)⋊C16, Dic491⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 83);