Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#559 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C17 |
| prime radical | C17×#127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,21)(20,24,25,23)(27,30)(31,32);(19,21)(23,24)(26,27,29,30)(28,32,33,31);(18,20,22,25)(19,23,21,24);(18,21,22,19)(20,24,25,23)(26,28,29,33)(27,31,30,32)425 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 240);