Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #99 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,6,8,7,2,4,3,9,5)(10,12)(11,14)(13,17)(15,16);(2,4)(3,7)(5,6)(8,9)(10,11)(12,16,17,14)(13,15)Polycyclic presentation:
2^5,3^2|a^2=c,f^3=g^2,b^a=bd,d^a=de,f^a=f^2g,g^a=g^2,c^b=ce51 conjugacy classes — view the full character table.
| maximal subgroup of | #10588149, #10588151, #10588152, … |
| maximal normal subgroup of | #10588149, #10588151, #10588152, … |
| maximal quotient of | #10588202, #10588203, #10588205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 41);