Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #2069⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#2069⋊C3 |
| unambiguous semidirect product | #2069⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2069)⋊C3 |
| Fitting, Hall | C5×#2069 ⋊ C3 |
| derived | #338 ⋊ C2×C3×C5 |
| Sylow | #2069 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #396⋊C3 |
| commutator, cosocle, hypocenter | #338 | C2×C3×C5 |
| Frattini | C22×C4 | C2×C5×A4 |
| Fitting | C5×#2069 | C3 |
| hypercenter | C4×C5 | #126⋊C3 |
| LCS | G ▷ #338 | |
| UCS | C1 ◁ C2×C5 ◁ C4×C5 | |
132 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 132 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)(7,11,8,14,20,17)(9,12)(13,21,16)(15,19,18);(6,21,9,20,10,15,12,11)(7,17,13,19,14,8,18,16)105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236394);