Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #63768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ #108 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,3,6)(2,5,4)(7,9,11,18,12,19,10,17)(8,13,14,16,15,21,20,22);(1,2)(3,5,6,4)(7,8,10,14,12,15,11,20)(9,16,17,21,19,22,18,13)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=d,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=fg^2,g^a=f^2g^2,f^c=f^2,g^c=g^230 conjugacy classes — view the full character table.
| maximal subgroup of | #10590018, #10590087, #10590137, … |
| maximal normal subgroup of | #10590018, #10590087, #10590137, … |
| maximal quotient of | #10590170, #10590173, #10590185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 418);