Finite Group DatabasebetaFinite Group Databasebeta| order | 5760 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting, socle | C24×C3 ⋊ S5 |
| derived | C3×#11757163 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#11757163 | C2 |
| Fitting, socle | C24×C3 | S5 |
| LCS | G ▷ C3×#11757163 | |
| UCS | C1 | |
450 conjugacy classes of subgroups; only the 7 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 7 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 30 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,7,3,4,2,9)(5,10)(11,12,13);(1,5,3,6)(2,7)(4,10,9,8)(12,13)30 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#11757163⋊C2, C2×#72275455 |
| maximal normal subgroup of | D3×#11757163⋊C2, C2×#72275455 |
| maximal quotient of | C2×#72275455 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,7,3,4,2,9)(5,10)(11,12,13), (1,5,3,6)(2,7)(4,10,9,8)(12,13));