Finite Group DatabasebetaFinite Group Databasebeta| order | 4310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C431⋊C5 |
| unambiguous semidirect product | (C2×C431)⋊C5 |
| Fitting, socle, Hall | C2×C431 ⋊ C5 |
| derived, Sylow | C431 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C431⋊C5 |
| commutator, cosocle, hypocenter | C431 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C431 | C5 |
| LCS | G ▷ C431 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 433 |
| transitive degree | μt(G) = 862 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C431⋊C5, D3×C431⋊C5, D5×C431⋊C5, … |
| maximal normal subgroup of | C2×C3×C431⋊C5, C2×C5×C431⋊C5, C2×C7×C431⋊C5 |
| maximal quotient of | C2×C3×C431⋊C5, D3×C431⋊C5, C2×C431⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4310, 2);