Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D53×C49⋊C3 |
| unambiguous semidirect product | C53⋊(C22×C49⋊C3) |
| unambiguous semidirect product | (C2×C53)⋊(C2×C49⋊C3) |
| unambiguous semidirect product | (C2×C49×D53)⋊C3 |
| Fitting | C2×C49×C53 ⋊ C2×C3 |
| derived, Hall | C49×C53 ⋊ C22×C3 |
| Hall | C2×C49×D53 ⋊ C3 |
| Hall | C53×C49⋊C3 ⋊ C22 |
| Sylow | C53 ⋊ C22×C49⋊C3 |
| Sylow | C49 ⋊ C2×C3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D53×C49⋊C3 |
| commutator, cosocle, hypocenter | C49×C53 | C22×C3 |
| Frattini | C7 | C2×ΓL(1,𝔽8)×D53 |
| Fitting | C2×C49×C53 | C2×C3 |
| socle | C2×C7×C53 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C49×C53 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5194 |
1064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 19);