Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
| direct product | #124×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C22 | C23×A5 |
| commutator, socle | C22×A5 | C23 |
| Fitting, hypercenter | #124 | A5 |
| prime radical | C2×D4×A5 | C2 |
| hypocenter | A5 | #124 |
| LCS | G ▷ C22×A5 ▷ A5 | |
| UCS | C1 ◁ C22 ◁ #124 | |
770 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | A5×H(3,𝔽4) |
| maximal normal subgroup of | A5×H(3,𝔽4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240531);