Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3788 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #97 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,3,6)(2,5,4)(7,8,9,10)(12,15)(16,18);(1,2)(3,5,6,4)(11,12,13,16,14,15,17,18)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=d,c^2=e,b^a=be,f^a=fg^2,g^a=f^2g^2,f^c=f^2,g^c=g^236 conjugacy classes — view the full character table.
| maximal subgroup of | #10590035, #10590036, #10590159, … |
| maximal normal subgroup of | #10590035, #10590036, #10590159, … |
| maximal quotient of | #10590149, #10590169, #10590179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 425);