Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23×C33 |
| direct product | C4×C3⋊(A4⋊S4) |
| Fitting | C24×C3×C4 ⋊ C3⋊D3 |
| derived | C3×A42 ⋊ C2×C4 |
1932 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1932 conjugacy classes of subgroups — too many to draw. Only its 131 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) = 108 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,4,3,2)(5,6,8,7)(10,11);(9,10,11)(12,13,14,15);(6,7,8);(2,3,4)(6,7,8)120 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#72213301 |
| maximal normal subgroup of | C4×#72213301 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,4,3,2)(5,6,8,7)(10,11), (9,10,11)(12,13,14,15), (6,7,8), (2,3,4)(6,7,8));