Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×C491⋊C8 |
| derived, Sylow | C491 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D491 |
| commutator, hypocenter | C491 | C22×C8 |
| Frattini | C4 | C22×D491 |
| Fitting | C22×C4×C491 | C2 |
| socle, prime radical | C23×C491 | C4 |
| cosocle | C4×C491 | C23 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
3952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536479, #44536480, #44536487, … |
| maximal normal subgroup of | #44536479, #44536480, #44536487, … |
| maximal quotient of | C2×C4×C491⋊C8, C2×C22⋊(C491⋊C8), C2×C4⋊(C491⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 148);