Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×#10596770⋊C2 |
| Fitting | C24×C4 ⋊ GO+(4,𝔽2) |
1987 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 1987 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 12 points:
(1,2,3,4)(6,10,11)(7,9,8);(7,9);(5,6)(7,12)(8,11)(9,10)80 conjugacy classes — view the full character table.
| automorphism group of | C5×H(5,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3,4)(6,10,11)(7,9,8), (7,9), (5,6)(7,12)(8,11)(9,10));