Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C22⋊C8 |
150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,4)(16,17,18);(1,2)(3,4)(5,6,7,9,8,10,11,12)(14,15)(17,18);(13,14,15)Polycyclic presentation:
2^5,3^2|a^2=c,c^2=e,b^a=bd,f^a=f^2,g^a=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10589145, #10589147, #10589149, … |
| maximal normal subgroup of | #10589145, #10589147, #10589149, … |
| maximal quotient of | #10589390, #10589391, #10589394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 305);