Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C53 · Schur multiplier (H2) = C2×C7 |
| direct product | D3×C53×C7⋊D7 |
| unambiguous semidirect product | (D3×C7)⋊(D7×C53) |
| Fitting, socle, Hall | C3×C72×C53 ⋊ C22 |
| derived, Hall | C3×C72 ⋊ C22×C53 |
| Hall | C72×C53 ⋊ C2×D3 |
| Hall | C3×C53 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×D3×C53 |
| Sylow | C3 ⋊ C2×C53×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D3×C7⋊D7 |
| commutator, cosocle, hypocenter | C3×C72 | C22×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C53 | C22 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C53 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7791 |
4134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 164);