Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3744 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ #108 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,3,5,12,6,13,4,11)(2,7,8,10,9,15,14,16)(20,21,22);(1,2,4,8,6,9,5,14)(3,10,11,15,13,16,12,7)(18,19)(21,22);(17,18,19)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=d,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10589121, #10589127, #10589130, … |
| maximal normal subgroup of | #10589121, #10589127, #10589130, … |
| maximal quotient of | #10589323, #10589324, #10589418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 294);