Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C3×C5×#353 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #99 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×D4 | C23×C3×C5 |
| prime radical | C2×C3×C5×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C23×C3×C5 ◁ C22×C3×C5×D4 ◁ G | |
736 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2)(11,12,13)(14,15,16,17,18);(3,4)(5,8,10,7)(6,9);(4,7)(5,10)(8,9)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 856);