Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #101 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 22 points:
(4,5,6)(7,9,11,17)(8,12,14,15)(10,18,19,16)(13,21,22,20);(2,3)(5,6)(7,8,10,13,11,14,19,22)(9,15,16,21,17,12,18,20);(1,2,3)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=e,c^2=e,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 | #10589182, #10589184, #10589343, … |
| maximal normal subgroup of | #10589182, #10589184, #10589343, … |
| maximal quotient of | #10589394, #10589396, #10589409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 311);