Finite Group DatabasebetaFinite Group Databasebeta| order | 4400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×AGL(1,𝔽5)×AGL(1,𝔽11) |
| Fitting, socle | C2×C5×C11 ⋊ C2×C4×C5 |
| derived | C5×C11 ⋊ C22×C4×C5 |
| Hall | C5×C11⋊C5 ⋊ C22×C4 |
| Sylow | C11 ⋊ C22×C5×AGL(1,𝔽5) |
226 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 110 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,8,5,11)(3,7,9,6,4)(12,13,14,15);(2,3)(4,6)(5,7)(8,11)(9,10);(13,14)(15,16)(17,18)110 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,8,5,11)(3,7,9,6,4)(12,13,14,15), (2,3)(4,6)(5,7)(8,11)(9,10), (13,14)(15,16)(17,18));