Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3788 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊#622 |
| Sylow | C32 ⋊ C4⋊C8 |
68 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);(1,2)(3,5,6,4)(8,10)(11,12,13,15,14,16,17,18)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=d,c^2=e,b^a=bd,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 | #10590037, #10590038, #10590039, … |
| maximal normal subgroup of | #10590037, #10590038, #10590039, … |
| maximal quotient of | C4⋊#3708, #10590170, #10590171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 424);