Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×D5×GL(2,ℤ/4) |
| Fitting | C24×C52 ⋊ C2×D3 |
| Sylow | C52 ⋊ C2×GL(2,ℤ/4) |
1208 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 1208 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 120 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,3,4)(6,8)(9,10,11,12,13)(14,15,17,18,16);(2,3)(5,6)(7,8);(15,16)(17,18)280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D5×A4⋊S4 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,3,4)(6,8)(9,10,11,12,13)(14,15,17,18,16), (2,3)(5,6)(7,8), (15,16)(17,18));