Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3714 |
| automorphism | Aut(G) = C22×D32×D4 (order 1152) · Inn(G) = #626 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #104 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 14 points:
(2,5,6,7)(10,11)(12,13,14);(1,2)(3,5)(4,6)(7,8)(9,10,11)(13,14)Polycyclic presentation:
2^5,3^2|b^2=c,d^2=e,b^a=bd,c^a=ce,d^a=de,g^a=g^2,f^b=f^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#805, #10590392, #10590915, … |
| maximal normal subgroup of | D3×#805, #10590392, #10590915, … |
| maximal quotient of | #10589081, #10589084, #10589086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 217);