Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #99 |
156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 14 points:
(4,5,6)(7,9)(8,11)(10,14)(12,13);(2,3)(5,6)(7,8)(9,13,14,11)(10,12);(1,2,3)Polycyclic presentation:
2^5,3^2|a^2=c,b^a=bd,d^a=de,f^a=f^2,g^a=g^2,c^b=ce51 conjugacy classes — view the full character table.
| maximal subgroup of | #10589173, #10589176, #10589178, … |
| maximal normal subgroup of | #10589173, #10589176, #10589178, … |
| maximal quotient of | #10589391, #10589392, #10589394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 309);