Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #85645 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#85645 |
| Fitting, Hall | C22×C5×#120 ⋊ C3 |
| derived | C26 ⋊ C2×C3×C5 |
| Sylow | C22×#120 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #85645 |
| commutator, cosocle, hypocenter | C26 | C2×C3×C5 |
| Frattini | C22 | C2×C5×C22⋊A4 |
| Fitting | C22×C5×#120 | C3 |
| socle | C24×C5 | C2×A4 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C5 | |
1648 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 1648 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) = 17 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,3,4,5)(7,9,8)(10,11)(12,14,16,15,13,17);(6,8)(7,9);(11,17)(14,15)120 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#85645 |
| maximal normal subgroup of | D5×#85645 |
| maximal quotient of | C5×#35346⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237081);