Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | A42×SD16 |
| Fitting, Sylow | C24×SD16 ⋊ C32 |
1295 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 1295 conjugacy classes of subgroups — too many to draw. Only its 77 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:
(1,4)(2,3)(5,8,6)(10,13)(11,15)(14,16);(2,4,3)(6,8,7)(9,10,11,13,12,14,15,16)112 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×A4⋊S4, A42×AGL(1,ℤ/8), #72228286, … |
| maximal normal subgroup of | SD16×A4⋊S4, A42×AGL(1,ℤ/8), #72228286, … |
| maximal quotient of | A42×#106 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,4)(2,3)(5,8,6)(10,13)(11,15)(14,16), (2,4,3)(6,8,7)(9,10,11,13,12,14,15,16));