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)(7,9,10,17,12,19,11,18)(8,13,20,22,15,21,14,16);(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=de,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 | #10590020, #10590021, #10590084, … |
| maximal normal subgroup of | #10590020, #10590021, #10590084, … |
| maximal quotient of | #10590171, #10590172, #10590185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 419);