Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ C4×D4 |
282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2,3,4)(6,8)(12,13,14);(5,6,7,8)(9,10,11);(6,8)(10,11)(13,14)Polycyclic presentation:
2^5,3^2|b^2=e,c^2=d,b^a=be,f^a=f^2,g^a=g^2,c^b=ce60 conjugacy classes — view the full character table.
| maximal subgroup of | #10590160, #10590430, #10590433, … |
| maximal normal subgroup of | #10590160, #10590430, #10590433, … |
| maximal quotient of | #10592353, #10592364, #10592365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 750);