Finite Group DatabasebetaFinite Group Databasebeta| order | 9600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#1020⋊AGL(1,𝔽5) |
| Fitting | C24×C52 ⋊ C4×D3 |
| derived | C5×C22⋊A4 ⋊ C2×C4×C5 |
| Sylow | C52 ⋊ #1020⋊C4 |
1020 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 18 points:
(2,7,6,5)(3,4)(9,10,11,12,13)(14,15,16,18,17);(1,2)(3,6,4,5,8,7)(15,16,17,18)190 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1020⋊AGL(1,𝔽5) |
| maximal normal subgroup of | D5×#1020⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,7,6,5)(3,4)(9,10,11,12,13)(14,15,16,18,17), (1,2)(3,6,4,5,8,7)(15,16,17,18));