Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×C5×#1929 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C2×D4 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle | C22×C3×C5 | C4×D4 |
| prime radical | C2×C3×C5×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G | |
448 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,6,7,8)(10,11)(13,14,17,21,18,16,25,20)(15,19,23,27,24,22,28,26);(9,10,12,11)(13,15,17,23,18,24,25,28)(14,19,21,27,16,22,20,26);(9,11,12,10)(13,16)(14,18)(15,22)(17,20)(19,24)(21,25)(23,26)(27,28)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 661);