Finite Group DatabasebetaFinite Group Databasebeta| order | 22698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3 |
| direct product | C3×C13×D97⋊C3 |
| unambiguous semidirect product | D97⋊(C32×C13) |
| unambiguous semidirect product | (C97⋊C3)⋊(C2×C3×C13) |
| unambiguous semidirect product | (C3×D97)⋊(C3×C13) |
| Fitting, socle | C3×C13×C97 ⋊ C2×C3 |
| derived, Sylow | C97 ⋊ C2×C32×C13 |
| Hall | C3×C13×C97⋊C3 ⋊ C2 |
| Hall | C13×D97 ⋊ C32 |
| Hall | C13×C97 ⋊ C2×C32 |
| Hall | C3×C97⋊C3 ⋊ C2×C13 |
| Hall | D97 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D97⋊C3 |
| commutator, cosocle, hypocenter | C97 | C2×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C97 | C2×C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C3×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3783 |
858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22698, 30);