Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C5×#85561 |
| derived | C22⋊A4 ⋊ C5×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5 | #1020 |
| commutator, hypocenter | C22⋊A4 | C5×C8 |
| Frattini | C4 | C5×#1020 |
| Fitting | C24×C4×C5 | D3 |
| socle | C25×C5 | Dic3 |
| prime radical | C2×C5×C22⋊A4 | C4 |
| cosocle | C4×C22⋊A4 | C2×C5 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C4×C5 | |
458 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 38 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) = 120 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(6,7,9,8)(10,11,13,12)(14,15,16,18,17,19,20,21);(7,8,9)(11,13,12)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236997);