Finite Group DatabasebetaFinite Group Databasebeta| order | 31605 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#20263466 |
| Fitting, Hall | C5×C43×C49 ⋊ C3 |
| derived, Hall | C43×C49 ⋊ C3×C5 |
| Hall | C5×C49 ⋊ C43⋊C3 |
| Hall | C5×C43 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ C5×C43⋊C3 |
| Sylow | C43 ⋊ C5×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #20263466 |
| commutator, cosocle, hypocenter | C43×C49 | C3×C5 |
| Frattini | C7 | C5×#11744748 |
| Fitting | C5×C43×C49 | C3 |
| socle | C5×C7×C43 | ΓL(1,𝔽8) |
| LCS | G ▷ C43×C49 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10535 |
3525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31605, 6);