Finite Group DatabasebetaFinite Group Databasebeta| order | 22692 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic1891 |
| derived, Hall | C31×C61 ⋊ C3×C4 |
| Hall | C3×C31×C61 ⋊ C4 |
| Hall | C3×C61 ⋊ Dic31 |
| Hall | C3×C31 ⋊ Dic61 |
| Sylow | C61 ⋊ C3×Dic31 |
| Sylow | C31 ⋊ C3×Dic61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1891 |
| commutator, hypocenter | C31×C61 | C3×C4 |
| Frattini | C2 | C3×D1891 |
| Fitting, socle, prime radical | C2×C3×C31×C61 | C2 |
| cosocle | C2×C31×C61 | C2×C3 |
| LCS | G ▷ C31×C61 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22692 |
5682 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22692, 8);