Finite Group DatabasebetaFinite Group Databasebeta| order | 22098 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D127⋊C3 |
| unambiguous semidirect product | D127⋊(C3×C29) |
| unambiguous semidirect product | (C127⋊C3)⋊(C2×C29) |
| unambiguous semidirect product | (C29×D127)⋊C3 |
| Fitting, socle, Hall | C29×C127 ⋊ C2×C3 |
| derived, Sylow | C127 ⋊ C2×C3×C29 |
| Hall | C29×C127⋊C3 ⋊ C2 |
| Hall | C29×D127 ⋊ C3 |
| Hall | C127⋊C3 ⋊ C2×C29 |
| Hall | D127 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D127⋊C3 |
| commutator, cosocle, hypocenter | C127 | C2×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C127 | C2×C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3683 |
783 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22098, 10);