Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4×D491 |
| Fitting | C22×C4×C491 ⋊ C2 |
| derived, Sylow | C491 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D491 |
| commutator, hypocenter | C491 | C23×C4 |
| Frattini | C2 | C23×D491 |
| Fitting | C22×C4×C491 | C2 |
| socle | C23×C491 | C22 |
| prime radical | C23×D491 | C2 |
| cosocle | C2×C491 | C24 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C22×C4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
3952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #95×D491, #44536572, C4×(C2×D491)⋊C4, … |
| maximal normal subgroup of | #95×D491, #44536572, C4×(C2×D491)⋊C4, … |
| maximal quotient of | C2×C42×D491, C22×C4×Dic491, C2×C22⋊C4×D491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 180);