Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Fitting | C2×C32×C4 ⋊ C4 |
| Sylow | C32 ⋊ #117 |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,3,6)(2,5,4)(8,12)(11,14);(7,9,10,13)(8,11,12,14);(1,2)(3,5,6,4)(7,8)(9,11)(10,12)(13,14)Polycyclic presentation:
2^5,3^2|a^2=d,b^2=e,c^a=ce,f^a=fg^2,g^a=f^2g^2,f^d=f^2,g^d=g^236 conjugacy classes — view the full character table.
| maximal subgroup of | #10590045, #10590048, #10590055, … |
| maximal normal subgroup of | #10590045, #10590048, #10590055, … |
| maximal quotient of | #10593725, #10593727, #10593730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 934);