Finite Group DatabasebetaFinite Group Databasebeta| order | 22164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D1847 |
| unambiguous semidirect product | C1847⋊(C22×C3) |
| unambiguous semidirect product | (C2×C1847)⋊(C2×C3) |
| Fitting, socle | C2×C3×C1847 ⋊ C2 |
| derived, Sylow | C1847 ⋊ C22×C3 |
| Hall | C3×C1847 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1847 |
| commutator, cosocle, hypocenter | C1847 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C1847 | C2 |
| LCS | G ▷ C1847 | |
| UCS | C1 ◁ C2×C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11082 |
5550 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22164, 8);