Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×Q16 ⋊ C2 |
| Sylow | C32 ⋊ #137 |
180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,3,5,9)(2,6,8,15)(4,13,14,11)(7,16,12,10)(20,21,22);(1,2,5,8)(3,10,9,16)(4,12,14,7)(6,13,15,11)(17,18,19);(3,9)(6,15)(10,16)(11,13)(18,19)(21,22)Polycyclic presentation:
2^5,3^2|b^2=e,c^2=e,d^2=e,c^a=ce,f^a=f^2,g^a=g^2,c^b=cd,d^b=de,d^c=de39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#918, #10594763, #10594766, … |
| maximal normal subgroup of | D3×#918, #10594763, #10594766, … |
| maximal quotient of | #10592488, #10592490, #10592493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 775);