Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Fitting | C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #117 |
228 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,3,4)(6,10)(7,11)(16,17,18);(5,7,8,11)(6,9,10,12)(13,14,15);(5,6)(7,9)(8,10)(11,12)(14,15)(17,18)Polycyclic presentation:
2^5,3^2|b^2=e,c^2=d,c^a=ce,f^a=f^2,g^a=g^2,c^b=ce60 conjugacy classes — view the full character table.
| maximal subgroup of | #10590164, #10590512, #10590513, … |
| maximal normal subgroup of | #10590164, #10590512, #10590513, … |
| maximal quotient of | #10592347, #10592350, #10592354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 749);