Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2192 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C5×#131 ◁ G | |
440 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,22)(12,26)(13,20)(14,19)(15,21)(16,23)(17,24)(18,29)(25,37)(27,38)(28,32)(30,36)(31,35)(33,40)(34,39);(9,11)(10,16)(12,27)(13,24)(14,31)(15,25)(17,32)(18,35)(19,33)(20,38)(21,34)(22,26)(23,29)(28,39)(30,40)(36,37);(9,11)(10,17)(12,23)(13,31)(14,24)(15,25)(16,32)(18,34)(19,37)(20,22)(21,35)(26,38)(27,29)(28,40)(30,39)(33,36)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 924);