Finite Group DatabasebetaFinite Group Databasebeta| order | 22068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D613 |
| Fitting, socle | C2×C32×C613 ⋊ C2 |
| derived, Sylow | C613 ⋊ C22×C32 |
| Hall | C32×C613 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D613 |
| commutator, cosocle, hypocenter | C613 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C613 | C2 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C2×C32 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11034 |
5544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22068, 57);