Finite Group DatabasebetaFinite Group Databasebeta| order | 11520 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C26 ⋊ C3×A5 |
| derived | #72235039 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | #72235039 | C3 |
| Frattini, socle | C24 | A4×A5 |
| Fitting, cosocle | C26 | C3×A5 |
| LCS | G ▷ #72235039 | |
| UCS | C1 | |
690 conjugacy classes of subgroups; only the 7 normal subgroups are shown.
This group has 690 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) = 20 |
| transitive degree | μt(G) = 20 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,15,20,7,10,6,16,17,12,4,2,13,19,9,8)(3,14,18,5,11);(1,3,2)(4,17)(5,16,7,14,9,13)(8,20,11,19,10,18)(12,15)28 conjugacy classes — view the full character table.
| derived subgroup of | #72240863 |
| maximal subgroup of | #72240863 |
| maximal normal subgroup of | #72240863 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,15,20,7,10,6,16,17,12,4,2,13,19,9,8)(3,14,18,5,11), (1,3,2)(4,17)(5,16,7,14,9,13)(8,20,11,19,10,18)(12,15));