Finite Group DatabasebetaFinite Group Databasebeta| order | 36414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C17 |
| direct product | C3×(C17⋊D17)⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C3×C17⋊D17)⋊ΓL(1,𝔽8) |
| Fitting, socle | C3×C7×C172 ⋊ C2×C3 |
| derived, Hall | C7×C172 ⋊ C2×C32 |
| Hall | C3×C7⋊(C172⋊C3) ⋊ C2 |
| Hall | C7×C17⋊D17 ⋊ C32 |
| Hall | C17⋊D17 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C172 ⋊ C2×C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×(C17⋊D17)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C17⋊D17)⋊ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7×C172 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C172 | C2×C3 |
| LCS | G ▷ C7×C172 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1071 |
1038 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36414, 85);