Finite Group DatabasebetaFinite Group Databasebeta| order | 264 |
| isoclinism | isoclinic class of #63140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C11 ⋊ Q8 |
| Sylow | C11 ⋊ Dic6 |
| Sylow | C3 ⋊ Dic22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D11 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C3×C11 | C22 |
| hypocenter | C3×C11 | Q8 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 264 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2,4,6,8,10,11,9,7,5,3)(13,14)(15,17,18,22)(16,19,20,21);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,14)(15,16,18,20)(17,21,22,19)Polycyclic presentation:
2^3,3,11|a^2=c,b^2=c,b^a=bc,e^a=e^10,d^b=d^239 conjugacy classes — view the full character table.
| maximal subgroup of | D11×Dic6, D3×Dic22, D33⋊Q8, … |
| maximal normal subgroup of | D11×Dic6, D3×Dic22, D33⋊Q8, … |
| maximal quotient of | Dic11⋊Dic3, #10587158, Dic3⋊Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(264, 11);