Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽5)×B(4,𝔽2)⋊C3 |
| Fitting | C5×B(4,𝔽2) ⋊ C3×C4 |
| derived | C5×H(5,𝔽2) ⋊ C2×C3×C4 |
| Hall | AGL(1,𝔽5)×B(4,𝔽2) ⋊ C3 |
| Sylow | C5 ⋊ C4×B(4,𝔽2)⋊C3 |
880 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 40 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) = 40 |
A minimal faithful permutation representation — 2 generators on 13 points:
(2,6,3)(5,8,7)(10,11,12,13);(1,6,4,8)(2,7)(3,5)(9,10,13,11,12)80 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#73026 |
| maximal normal subgroup of | AGL(1,𝔽5)×#73026 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,6,3)(5,8,7)(10,11,12,13), (1,6,4,8)(2,7)(3,5)(9,10,13,11,12));