Finite Group DatabasebetaFinite Group Databasebeta| order | 264 |
| isoclinism | isoclinic class of #63140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C11 ⋊ D4 |
| Sylow | C11 ⋊ D12 |
| Sylow | C3 ⋊ C22⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D11 |
| commutator, Fitting, socle, cosocle | C2×C3×C11 | C22 |
| hypocenter | C3×C11 | D4 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2 | |
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)(13,14)(16,18);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,14)(15,16,17,18)Polycyclic presentation:
2^3,3,11|a^2=c,b^a=bc,e^a=e^10,d^b=d^239 conjugacy classes — view the full character table.
| maximal subgroup of | #10587230, #10587231, #10587233, … |
| maximal normal subgroup of | #10587230, #10587231, #10587233, … |
| maximal quotient of | #10587143, #10587148, #10587149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(264, 10);