Finite Group DatabasebetaFinite Group Databasebeta| order | 31458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×D749 |
| unambiguous semidirect product | C107⋊(D7×ΓL(1,𝔽8)) |
| Fitting, socle, derived, Hall | C72×C107 ⋊ C2×C3 |
| Hall | C7×ΓL(1,𝔽8)×C107 ⋊ C2 |
| Hall | C7×D749 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ D107 |
| Sylow | C107 ⋊ D7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C3×D107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C107 | C2×C3 |
| LCS | G ▷ C72×C107 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4494 |
1880 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31458, 22);