Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5×C7 · Schur multiplier (H2) = C24 |
| direct product | C2×C5×C7×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5×C7 | C22 |
| commutator | C2 | C22×C4×C5×C7 |
| Frattini, cosocle | C22 | C23×C5×C7 |
| prime radical | C24×C5×C7 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5×C7 ◁ G | |
264 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 560 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2)(11,12,13,14,15)(16,17,18,19,20,21,22);(3,4,6,8)(5,7,9,10);(4,7)(8,10)700 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 891);