Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#444 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×D4 |
| commutator | C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C4 | C23×C17 |
| socle | C2×C17 | C4×D4 |
| prime radical | C17×#135 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C8×C17 ◁ G | |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,26,23,20,27,25)(21,28,29,32,30,24,31,33);(18,20)(19,23)(21,28)(22,25)(24,30)(26,27)(29,32)(31,33);(18,21,22,29,23,30,27,31)(19,24,26,33,20,28,25,32)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 125);