Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×C11×#117 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5×C11 | C22 |
| commutator | C2 | C22×C4×C5×C11 |
| Frattini, cosocle | C22 | C23×C5×C11 |
| socle | C22×C5×C11 | C23 |
| prime radical | C23×C5×C11 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5×C11 ◁ G | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 880 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20)(21,22)(23,26)(24,25)(27,28);(22,25)(26,28);(21,23,24,27)(22,26,25,28)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1065);