Finite Group DatabasebetaFinite Group Databasebeta| order | 4310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D431⋊C5 |
| unambiguous semidirect product | (C431⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C431 ⋊ C2×C5 |
| Hall | C431⋊C5 ⋊ C2 |
| Hall | D431 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C431 | C2×C5 |
| LCS | G ▷ C431 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 431 |
| transitive degree | μt(G) = 431 |
Polycyclic presentation:
2,5,431|c^a=c^430,c^b=c^9553 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D431⋊C5, C3⋊(D431⋊C5), C5×D431⋊C5, … |
| maximal normal subgroup of | C3×D431⋊C5, C5×D431⋊C5, C7×D431⋊C5 |
| maximal quotient of | C3×D431⋊C5, C3⋊(D431⋊C5), D431⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4310, 1);