Finite Group DatabasebetaFinite Group Databasebeta| order | 36162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C41 · Schur multiplier (H2) = C3 |
| direct product | C3×C41×ΓL(1,𝔽8)⋊D7 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3×D7×C41) |
| Fitting, socle | C3×C72×C41 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C32×C41 |
| Hall | C3×C7×ΓL(1,𝔽8)×C41 ⋊ C2 |
| Hall | C41×C7⋊D7 ⋊ C32 |
| Hall | C72×C41 ⋊ C2×C32 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C2×C41 |
| Hall | C7⋊D7 ⋊ C32×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | ΓL(1,𝔽8)⋊D7 |
| commutator, cosocle, hypocenter | C72 | C2×C32×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C41 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C41 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2583 |
2706 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36162, 81);