Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C53⋊#64418 |
| unambiguous semidirect product | (C2×C53)⋊#64418 |
| Fitting, socle | C2×C72×C53 ⋊ D3 |
| derived, Hall | C53×#3862 ⋊ C22 |
| Hall | C72×C53 ⋊ C2×D3 |
| Hall | #3862 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×#64418 |
| Sylow | C72 ⋊ C2×D159 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C53⋊#64418 |
| commutator, cosocle, hypocenter | C53×#3862 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C53 | D3 |
| LCS | G ▷ C53×#3862 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1484 |
1028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 115);