Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | Aut(G) = D32×#120 (order 1152) · Inn(G) = (C2×D3)⋊Dic3 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #99 |
121 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 121 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 14 points:
(2,3)(4,5,6)(7,9)(8,11,12,13)(10,14);(1,2,3)(5,6)(7,8)(9,13)(10,12)(11,14)Polycyclic presentation:
2^5,3^2|b^2=c,b^a=bd,c^a=ce,g^a=g^2,d^b=de,f^b=f^239 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#806, #10590404, #10590405, … |
| maximal normal subgroup of | D3×#806, #10590404, #10590405, … |
| maximal quotient of | #10589145, #10589147, #10589149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 228);