Finite Group DatabasebetaFinite Group Databasebeta| order | 17457 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C232⋊C3)⋊C11 |
| unambiguous semidirect product | #19154120⋊C3 |
| Fitting, socle, derived, Sylow | C232 ⋊ C3×C11 |
| Hall | #19154120 ⋊ C3 |
| Hall | C232⋊C3 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C232 | C3×C11 |
| LCS | G ▷ C232 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 69 |
Polycyclic presentation:
3,11,23^2|c^a=c^6d^18,d^a=c^4d^16,c^b=c^2,d^b=d^249 conjugacy classes — view the full character table.
| maximal subgroup of | #15691772⋊C11, ((C23⋊D23)⋊C3)⋊C11, C2×(C232⋊C3)⋊C11 |
| maximal normal subgroup of | #15691772⋊C11, ((C23⋊D23)⋊C3)⋊C11, C2×(C232⋊C3)⋊C11 |
| maximal quotient of | C2×(C232⋊C3)⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17457, 4);