Finite Group DatabasebetaFinite Group Databasebeta| order | 38514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C131 · Schur multiplier (H2) = C1 |
| direct product | C131×ΓL(1,𝔽8)⋊D7 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(D7×C131) |
| Fitting, socle, Hall | C72×C131 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C3×C131 |
| Hall | C7×ΓL(1,𝔽8)×C131 ⋊ C2 |
| Hall | C7⋊D7×C131 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×C131 |
| Hall | C7⋊D7 ⋊ C3×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C131 | ΓL(1,𝔽8)⋊D7 |
| commutator, cosocle, hypocenter | C72 | C2×C3×C131 |
| Frattini | C1 | G |
| Fitting, socle | C72×C131 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C131 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2751 |
2882 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38514, 19);