Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C53 · Schur multiplier (H2) = C2 |
| Fitting, Hall | C22×C49×C53 ⋊ C3 |
| derived, Hall | C22×C49 ⋊ C3×C53 |
| Hall | C49×C53 ⋊ A4 |
| Hall | C22×C53 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ A4×C53 |
| Sylow | C22 ⋊ C53×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | C22⋊(C49⋊C3) |
| commutator, cosocle, hypocenter | C22×C49 | C3×C53 |
| Frattini | C7 | C53×C22⋊ΓL(1,𝔽8) |
| Fitting | C22×C49×C53 | C3 |
| socle | C22×C7×C53 | ΓL(1,𝔽8) |
| LCS | G ▷ C22×C49 | |
| UCS | C1 ◁ C53 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10388 |
3604 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 33);