Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C2×C32×D4 ⋊ C2 |
| Sylow | C32 ⋊ AGL(1,ℤ/8) |
204 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 14 points:
(2,7)(3,4)(6,8)(12,13,14);(1,3,5,4)(2,6,8,7)(9,10,11);(1,2)(3,6)(4,7)(5,8)(10,11)(13,14)Polycyclic presentation:
2^5,3^2|b^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^2,g^a=g^2,c^b=ce,d^c=de51 conjugacy classes — view the full character table.
| maximal subgroup of | #10591406, #10591407, #10591523, … |
| maximal normal subgroup of | #10591406, #10591407, #10591523, … |
| maximal quotient of | #10592663, #10592665, #10592667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 789);