Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#85550 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C5 | #1020 |
| commutator, cosocle, hypocenter | #543⋊C3 | C2×C5 |
| Frattini | C22 | C5×#1020 |
| Fitting | C5×#543 | D3 |
| prime radical | C5×#543⋊C3 | C2 |
| LCS | G ▷ #543⋊C3 | |
| UCS | C1 ◁ C22×C5 | |
220 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5)(6,7,11,8,9,12,13,10)(14,19,28,20)(15,23,29,24)(16,25,17,21)(18,26,22,27);(7,11,8)(10,12,13)(16,17,22)(19,20,25)(23,24,28)(26,27,29)105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236986);