Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#85546 |
| Fitting | C26×C5 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C22×S4 |
| commutator, cosocle | C22×A4 | C23×C5 |
| Frattini | C22 | C22×C5×S4 |
| Fitting | C26×C5 | D3 |
| socle | C24×C5 | C22×D3 |
| hypercenter | C24×C5 | S4 |
| hypocenter | A4 | C5×#120 |
| LCS | G ▷ C22×A4 ▷ A4 | |
| UCS | C1 ◁ C22×C5 ◁ C24×C5 | |
1888 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 1888 conjugacy classes of subgroups — too many to draw. Only its 112 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)(14,15,17);(11,13);(6,7)(8,9)(10,11)(12,13)(15,16)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236982);