Finite Group DatabasebetaFinite Group Databasebeta| order | 22218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C7⋊(C232⋊C3) |
| unambiguous semidirect product | (C2×C7)⋊(C232⋊C3) |
| unambiguous semidirect product | (C2×C232)⋊ΓL(1,𝔽8) |
| Fitting, socle, Hall | C2×C7×C232 ⋊ C3 |
| derived, Hall | C7×C232 ⋊ C2×C3 |
| Hall | C2×C232 ⋊ ΓL(1,𝔽8) |
| Sylow | C232 ⋊ C2×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C232⋊C3 |
| Sylow | C7 ⋊ C2×C232⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊(C232⋊C3) |
| commutator, cosocle, hypocenter | C7×C232 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C232 | C3 |
| LCS | G ▷ C7×C232 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 966 |
2474 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22218, 28);