Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×#85547 |
| Fitting | C22×C43 ⋊ D3 |
| derived | C22⋊(C42⋊C3) ⋊ C2×C4 |
1845 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 1845 conjugacy classes of subgroups — too many to draw. Only its 32 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) = 24 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,4,2,3)(5,9,7,6)(8,15,10,14,11,16,12,13);(2,3,4)(5,10,13,9,8,16,7,12,14,6,11,15)96 conjugacy classes — view the full character table.
| maximal subgroup of | #72239370, C4×#72209990 |
| maximal quotient of | C4×#72209990 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,4,2,3)(5,9,7,6)(8,15,10,14,11,16,12,13), (2,3,4)(5,10,13,9,8,16,7,12,14,6,11,15));