Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3714 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#3716 |
| Sylow | C32 ⋊ C2×SD16 |
155 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 155 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 96 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2)(4,5)(6,7,8)(9,10,11,13,12,14,15,16);(3,4,5)(7,8)(10,13)(11,15)(14,16);(1,2)48 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#3716, #10590360, #10590365, … |
| maximal normal subgroup of | C4×#3716, #10590360, #10590365, … |
| maximal quotient of | #10590268, #10590273, #10590288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 476);