Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D3×C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C8 · Schur multiplier (H2) = C1 |
| direct product | C3⋊C8×C11⋊C5 |
| unambiguous semidirect product | C3⋊(C8×C11⋊C5) |
| unambiguous semidirect product | (C11×C3⋊C8)⋊C5 |
| derived, Hall | C3×C11 ⋊ C5×C8 |
| Hall | C11×C3⋊C8 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C8 |
| Sylow | C11 ⋊ C5×C3⋊C8 |
| Sylow | C3 ⋊ C8×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×C11⋊C5 |
| commutator, hypocenter | C3×C11 | C5×C8 |
| Fitting, cosocle | C3×C4×C11 | C2×C5 |
| socle | C2×C3×C11 | C4×C5 |
| prime radical | C2×C3×C11⋊C5 | C4 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C4 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 264 |
A minimal faithful permutation representation — 2 generators on 22 points:
(2,3)(4,5,6,8,7,9,10,11)(13,14,16,19,18)(15,17,21,22,20);(1,2,3)(12,13,15,18,14,16,20,22,17,19,21)84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C8×C11⋊C5, ΓL(1,𝔽25)×C11⋊C5, #72216797, … |
| maximal normal subgroup of | D3×C8×C11⋊C5, ΓL(1,𝔽25)×C11⋊C5, #72216797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 2);