Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#2238 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C3×C5×#469 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C2×C3×C5×M16 ◁ G | |
268 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,7,8)(10,14)(11,17)(12,20)(15,22)(16,19)(18,24)(21,23);(11,18)(14,22)(17,24)(19,23);(9,10,12,21,13,15,20,16)(11,19,17,22,18,23,24,14)300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 970);