Finite Group DatabasebetaFinite Group Databasebeta| order | 14570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D47×ΓL(1,𝔽32) |
| unambiguous semidirect product | C47⋊(C2×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×D47)⋊C5 |
| Fitting, socle, derived, Hall | C31×C47 ⋊ C2×C5 |
| Hall | C47×ΓL(1,𝔽32) ⋊ C2 |
| Hall | C31×D47 ⋊ C5 |
| Sylow | C47 ⋊ C2×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C5×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C47 | C2×C5 |
| LCS | G ▷ C31×C47 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1457 |
275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D31⋊C5, C2×D47×ΓL(1,𝔽32) |
| maximal normal subgroup of | D47×D31⋊C5, C2×D47×ΓL(1,𝔽32) |
| maximal quotient of | ΓL(1,𝔽32)×Dic47, C2×D47×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14570, 10);