Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C2×C32×C8 ⋊ C2 |
| Sylow | C32 ⋊ #131 |
186 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,3,4,9,5,10,11,15)(2,7,8,14,6,12,13,16)(20,21,22);(2,6)(7,12)(8,13)(14,16)(17,18,19);(1,2)(3,7)(4,8)(5,6)(9,14)(10,12)(11,13)(15,16)(18,19)(21,22)Polycyclic presentation:
2^5,3^2|c^2=d,d^2=e,b^a=be,f^a=f^2,g^a=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10589113, #10589374, #10589381, … |
| maximal normal subgroup of | #10589113, #10589374, #10589381, … |
| maximal quotient of | C8×#634, #10592378, C8×C4⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 758);