Finite Group DatabasebetaFinite Group Databasebeta| order | 33579 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C41 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C7×C13×C41 ⋊ C32 |
| derived, Hall | C7×C13 ⋊ C32×C41 |
| Hall | C13×C41 ⋊ C3×ΓL(1,𝔽8) |
| Hall | C7×C41 ⋊ C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×ΓL(1,𝔽8)×C41 |
| Sylow | C7 ⋊ C3×C13⋊C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | ΓL(1,𝔽8)×C13⋊C3 |
| commutator, cosocle, hypocenter | C7×C13 | C32×C41 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C41 | C32 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C41 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3731 |
1435 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33579, 7);