Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C32×C8 ⋊ C22 |
| Sylow | C32 ⋊ C2×SD16 |
147 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2,3,5,4,6,7,8)(9,10,11)(12,13,14);(2,5)(3,7)(6,8)(10,11);(2,5)(3,7)(6,8)(13,14)Polycyclic presentation:
2^5,3^2|c^2=d,d^2=e,c^a=cd,d^a=de,g^a=g^2,c^b=cd,d^b=de,f^b=f^236 conjugacy classes — view the full character table.
| maximal subgroup of | #10593284, #10593286, #10593291, … |
| maximal normal subgroup of | #10593284, #10593286, #10593291, … |
| maximal quotient of | #10590649, #10590672, #10590685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 444);