Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×C4×SO(3,𝔽7) |
| derived | GL(3,𝔽2) ⋊ C2×C3×C4 |
265 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2,3)(4,5,6,7)(9,14,15)(10,11,12);(1,2,3)(8,9,10,14,11,13)108 conjugacy classes — view the full character table.
| maximal quotient of | C3×C4×#10621462 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(4,5,6,7)(9,14,15)(10,11,12), (1,2,3)(8,9,10,14,11,13));