Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #117 |
179 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 18 points:
(5,7,8,12)(6,9,10,11)(13,14,15)(16,17,18);(1,3,4,2)(7,12)(9,11)(14,15);(1,2,4,3)(5,6,8,10)(7,11,12,9)(17,18)Polycyclic presentation:
2^5,3^2|a^2=d,b^2=de,c^2=e,c^a=ce,g^a=g^2,c^b=ce,f^b=f^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10590045, #10590056, #10590450, … |
| maximal normal subgroup of | #10590045, #10590056, #10590450, … |
| maximal quotient of | #10590256, #10590257, #10590260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 497);