Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ #108 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,3,4,12,6,13,5,14)(2,7,8,11,10,15,9,16)(20,21,22);(1,2,5,9,6,10,4,8)(3,11,12,15,13,16,14,7)(18,19)(21,22);(17,18,19)Polycyclic presentation:
2^5,3^2|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bd,f^a=f^2,g^a=g^2,d^b=de54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#822, #10590973, #10590975, … |
| maximal normal subgroup of | D3×#822, #10590973, #10590975, … |
| maximal quotient of | #10589345, #10589346, #10589424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 297);