Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3744 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #106 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 288 |
A minimal faithful permutation representation — 3 generators on 18 points:
(5,6,7,9,8,10,11,12)(16,17,18);(1,2,3,4)(6,9)(7,11)(10,12)(14,15)(17,18);(13,14,15)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=d,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10589124, #10589137, #10589360, … |
| maximal normal subgroup of | #10589124, #10589137, #10589360, … |
| maximal quotient of | #10589323, #10589379, #10589417, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 292);