Finite Group DatabasebetaFinite Group Databasebeta| order | 27678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×D659 |
| unambiguous semidirect product | C659⋊(C2×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×D659)⋊C3 |
| Fitting, socle, derived, Hall | C7×C659 ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)×C659 ⋊ C2 |
| Hall | C7×D659 ⋊ C3 |
| Sylow | C659 ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×D659 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C659 | C2×C3 |
| LCS | G ▷ C7×C659 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4613 |
1655 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27678, 14);