Finite Group DatabasebetaFinite Group Databasebeta| order | 18678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D283⋊C3) |
| unambiguous semidirect product | (C283⋊C3)⋊D11 |
| unambiguous semidirect product | D3113⋊C3 |
| Fitting, socle, derived, Hall | C11×C283 ⋊ C2×C3 |
| Hall | C11×C283⋊C3 ⋊ C2 |
| Hall | D3113 ⋊ C3 |
| Hall | C283⋊C3 ⋊ D11 |
| Sylow | C283 ⋊ C3×D11 |
| Sylow | C11 ⋊ D283⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C283 | C2×C3 |
| LCS | G ▷ C11×C283 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3113 |
Polycyclic presentation:
2,3,11,283|c^a=c^10,d^a=d^282,d^b=d^238538 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D283⋊C3, C2×C11⋊(D283⋊C3) |
| maximal normal subgroup of | D11×D283⋊C3, C2×C11⋊(D283⋊C3) |
| maximal quotient of | C11⋊((C283⋊C3)⋊C4), C2×C11⋊(D283⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18678, 12);