Finite Group DatabasebetaFinite Group Databasebeta| order | 22698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C97 · Schur multiplier (H2) = C3 |
| direct product | C32×D13×C97 |
| Fitting, socle, Hall | C32×C13×C97 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C32×C97 |
| Hall | C13×C97 ⋊ C2×C32 |
| Hall | C32×C13 ⋊ C2×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C97 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C32×C97 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C97 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C32×C97 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11349 |
6984 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22698, 63);