Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C2 |
| direct product | A4×#7333 |
| Fitting, Sylow | C22×#7333 ⋊ C3 |
411 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 411 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 36 points:
(2,4,3)(5,7,8,14,10,19,23,15,11,20,24,18,29,35,36,16,12,21,25,28,9,26,22,33,27,13,30,31,17,32,34,6);(1,4)(2,3)(5,6,8,13,9,14,22,32,11,15,24,7,17,18,34,19,12,16,25,20,10,28,23,35,27,33,30,21,29,31,36,26)184 conjugacy classes — view the full character table.
| maximal subgroup of | A4×AGL(1,ℤ/32), S4×#7333, #72343039 |
| maximal normal subgroup of | A4×AGL(1,ℤ/32), S4×#7333, #72343039 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,4,3)(5,7,8,14,10,19,23,15,11,20,24,18,29,35,36,16,12,21,25,28,9,26,22,33,27,13,30,31,17,32,34,6), (1,4)(2,3)(5,6,8,13,9,14,22,32,11,15,24,7,17,18,34,19,12,16,25,20,10,28,23,35,27,33,30,21,29,31,36,26));