Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×C3⋊#6157 |
| unambiguous semidirect product | C3⋊(C72×#6157) |
| Fitting, socle, Hall | C3×C72×C53 ⋊ C4 |
| derived, Hall | C3×C53 ⋊ C4×C72 |
| Hall | C72×C53 ⋊ Dic3 |
| Hall | C3×C72 ⋊ #6157 |
| Sylow | C53 ⋊ C72×Dic3 |
| Sylow | C3 ⋊ C72×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C3⋊#6157 |
| commutator, hypocenter | C3×C53 | C4×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C53 | C4 |
| prime radical | C3×C72×D53 | C2 |
| cosocle | C3×D53 | C2×C72 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C72 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7791 |
2205 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 147);