Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5×C7 · Schur multiplier (H2) = C23 |
| direct product | C5×C7×#95 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C5×C7 | C22 |
| commutator | C2 | C42×C5×C7 |
| Frattini, cosocle | C23 | C22×C5×C7 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5×C7 ◁ G | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 1120 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(6,7,8,9,10,11,12)(18,20)(21,22,24,23);(13,14,15,16)(17,18,19,20)(21,23,24,22)700 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 197);