Finite Group DatabasebetaFinite Group Databasebeta| order | 23298 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D353⋊C11) |
| unambiguous semidirect product | D1059⋊C11 |
| unambiguous semidirect product | (C353⋊C11)⋊D3 |
| Fitting, socle, derived, Hall | C3×C353 ⋊ C2×C11 |
| Hall | C3×C353⋊C11 ⋊ C2 |
| Hall | C353⋊C11 ⋊ D3 |
| Hall | D1059 ⋊ C11 |
| Sylow | C353 ⋊ D3×C11 |
| Sylow | C3 ⋊ D353⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C353 | C2×C11 |
| LCS | G ▷ C3×C353 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1059 |
Polycyclic presentation:
2,3,11,353|b^a=b^2,d^a=d^352,d^c=d^14081 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23298, 12);