Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#461 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C17 |
| prime radical | C2×D4×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,25,28)(24,26,29,27);(18,19,20,21);(23,26)(24,29)(27,28)323 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 142);