Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #85646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#85646 |
| Fitting, Hall | C22×C5×#126 ⋊ C3 |
| derived | C22×C42 ⋊ C2×C3×C5 |
| Sylow | C22×#126 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #85646 |
| commutator, cosocle, hypocenter | C22×C42 | C2×C3×C5 |
| Frattini | C22 | C2×C5×C22⋊A4 |
| Fitting | C22×C5×#126 | C3 |
| socle | C24×C5 | C2×A4 |
| LCS | G ▷ C22×C42 | |
| UCS | C1 ◁ C5 | |
520 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,3,4,5)(7,8,9)(11,22,24,15,16,18)(12,25,23,20,21,19)(13,14,17);(6,9)(7,8)(10,13)(11,15)(12,16)(14,17)(18,21)(19,23)(20,22)(24,25);(10,18,14,25)(11,22,19,16)(12,15,20,23)(13,21,17,24)120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237082);