Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C72×C53 · Schur multiplier (H2) = C2×C7 |
| direct product | C72×A4×C53 |
| unambiguous semidirect product | C22⋊(C3×C72×C53) |
| unambiguous semidirect product | (C22×C53)⋊(C3×C72) |
| Fitting, socle, Hall | C22×C72×C53 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C72×C53 |
| Hall | C22×C53 ⋊ C3×C72 |
| Hall | C22×C72 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72×C53 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C72×C53 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C53 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C72×C53 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10388 |
10388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 168);