Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#85551 |
| Fitting | C5×#543 ⋊ D3 |
| derived | #543⋊C3 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C5 | #1020 |
| commutator, cosocle, hypocenter | #543⋊C3 | C2×C5 |
| Frattini | C22 | C5×#1020 |
| Fitting | C5×#543 | D3 |
| LCS | G ▷ #543⋊C3 | |
| UCS | C1 ◁ C22×C5 | |
340 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 340 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) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(6,20,12,8,10,13,16,11)(7,21,18,9,14,19,15,17);(7,12,8)(11,14,16)(13,19,15)(18,20,21)105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236987);