Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | A4×(C2×S4)⋊C4 |
| Fitting | C25×C4 ⋊ C3×D3 |
2125 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 2125 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,4,3)(5,8,6)(9,10,11,12)(14,16);(1,4)(2,3)(7,8)(13,14)(15,16)112 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((2,4,3)(5,8,6)(9,10,11,12)(14,16), (1,4)(2,3)(7,8)(13,14)(15,16));