Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #63653 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ Q32 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 288 |
A minimal faithful permutation representation — 3 generators on 38 points:
(1,3,6,14)(2,7,10,24)(4,16,19,32)(5,21,17,13)(8,26,27,31)(9,28,20,23)(11,29,30,15)(12,25,22,18)(36,37,38);(1,2,6,10)(3,11,14,30)(4,15,19,29)(5,20,17,9)(7,22,24,12)(8,25,27,18)(13,31,21,26)(16,28,32,23)(34,35)(37,38);(33,34,35)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=g^2,c^b=cd,d^b=de39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#829, #10591042, #10591045, … |
| maximal normal subgroup of | D3×#829, #10591042, #10591045, … |
| maximal quotient of | #10589355, #10589358, #10589430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 304);