Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C22×C42 |
| direct product | C17×H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
260 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
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)(18,19,22,25)(20,27,28,24)(21,29,31,33)(23,26,32,30);(18,20,22,28)(19,24,25,27)(21,30,31,26)(23,29,32,33);(18,21)(19,20)(22,31)(23,24)(25,28)(26,29)(27,32)(30,33);(18,20)(19,21)(22,28)(23,29)(24,26)(25,31)(27,30)(32,33)323 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 242);