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 ⋊ #100 |
138 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)(8,11)(9,13);(2,3)(5,6)(7,8,9,12,10,11,13,14);(1,2,3)Polycyclic presentation:
2^5,3^2|a^2=c,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 | #10589172, #10589175, #10589337, … |
| maximal normal subgroup of | #10589172, #10589175, #10589337, … |
| maximal quotient of | #10589391, #10589396, #10589406, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 308);