Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ((C23⋊D23)⋊C3)⋊C11 |
| unambiguous semidirect product | #26042787⋊C3 |
| Fitting, socle, derived, Sylow | C232 ⋊ C2×C3×C11 |
| Hall | (C232⋊C3)⋊C11 ⋊ C2 |
| Hall | #26042787 ⋊ C3 |
| Hall | #19154120 ⋊ C2×C3 |
| Hall | (C23⋊D23)⋊C3 ⋊ C11 |
| Hall | C232⋊C3 ⋊ C2×C11 |
| Hall | C23⋊D23 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C232 | C2×C3×C11 |
| LCS | G ▷ C232 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 69 |
Polycyclic presentation:
2,3,11,23^2|d^a=d^22,e^a=e^22,d^b=d^7e^17,e^b=d^21e^15,d^c=d^12,e^c=e^1274 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 15);