Finite Group DatabasebetaFinite Group Databasebeta| order | 264 |
| isoclinism | isoclinic class of Dic66 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×C3×C11 ⋊ C2 |
| Hall | C3×C11 ⋊ D4 |
| Sylow | C11 ⋊ #67 |
| Sylow | C3 ⋊ C22⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D33 |
| commutator, socle, cosocle | C2×C3×C11 | C22 |
| Fitting | C22×C3×C11 | C2 |
| hypercenter | C22 | D33 |
| hypocenter | C3×C11 | D4 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2 ◁ C22 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 132 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,4,6,8,10,11,9,7,5,3)(12,13,14)(16,18);(2,3)(4,5)(6,7)(8,9)(10,11)(13,14)(15,16)(17,18)Polycyclic presentation:
2^3,3,11|b^a=bc,d^a=d^2,e^a=e^1069 conjugacy classes — view the full character table.
| maximal subgroup of | #10587241, #10587244, D11×#67, … |
| maximal normal subgroup of | #10587241, #10587244, D11×#67, … |
| maximal quotient of | #10587201, #10587203, #10587204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(264, 27);