Finite Group DatabasebetaFinite Group Databasebeta| order | 22098 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊(D127⋊C3) |
| unambiguous semidirect product | (C127⋊C3)⋊D29 |
| unambiguous semidirect product | D3683⋊C3 |
| Fitting, socle, derived, Hall | C29×C127 ⋊ C2×C3 |
| Hall | C29×C127⋊C3 ⋊ C2 |
| Hall | D3683 ⋊ C3 |
| Hall | C127⋊C3 ⋊ D29 |
| Sylow | C127 ⋊ C3×D29 |
| Sylow | C29 ⋊ D127⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C127 | C2×C3 |
| LCS | G ▷ C29×C127 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3683 |
Polycyclic presentation:
2,3,29,127|c^a=c^28,d^a=d^126,d^b=d^107657 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22098, 12);