Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×#5997⋊C3 |
| unambiguous semidirect product | #5997⋊(C3×C53) |
| unambiguous semidirect product | (C53×#5997)⋊C3 |
| Fitting, socle, Hall | C72×C53 ⋊ C3×C4 |
| derived, Sylow | C72 ⋊ C3×C4×C53 |
| Hall | C53×#5997 ⋊ C3 |
| Hall | C53×#3861 ⋊ C4 |
| Hall | #5997 ⋊ C3×C53 |
| Hall | #3861 ⋊ C4×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | #5997⋊C3 |
| commutator, hypocenter | C72 | C3×C4×C53 |
| Frattini | C1 | G |
| Fitting, socle | C72×C53 | C3×C4 |
| prime radical | C53×#64424 | C2 |
| cosocle | C7⋊D7 | C2×C3×C53 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C53 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 742 |
848 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 81);