Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3035 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| socle | C22×C3×C5 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C2×C3×C42×C5 ◁ G | |
992 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7,8)(10,12)(13,14)(15,22)(16,20)(17,25)(18,21)(19,23)(24,27)(26,28);(9,10,11,12);(13,15)(14,19)(16,23)(17,26)(18,24)(20,27)(21,28)(22,25);(13,16,18,17)(14,20,21,25)(15,23,24,26)(19,27,28,22)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1767);