Finite Group DatabasebetaFinite Group Databasebeta| order | 8620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C4×C431⋊C5 |
| unambiguous semidirect product | (C4×C431)⋊C5 |
| Fitting, Hall | C4×C431 ⋊ C5 |
| derived, Sylow | C431 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C431⋊C5 |
| commutator, hypocenter | C431 | C4×C5 |
| Frattini | C2 | C2×C431⋊C5 |
| Fitting | C4×C431 | C5 |
| socle | C2×C431 | C2×C5 |
| LCS | G ▷ C431 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
364 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×C431⋊C5, Dic3×C431⋊C5 |
| maximal normal subgroup of | C3×C4×C431⋊C5 |
| maximal quotient of | C3×C4×C431⋊C5, Dic3×C431⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8620, 3);