Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11751539 |
| derived | SL(2,𝔽5) ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×A5 |
| commutator, hypocenter | SL(2,𝔽5) | C22×C4 |
| Frattini, cosocle | C22 | C23×A5 |
| Fitting, hypercenter | C2×C4⋊C4 | A5 |
| prime radical | C22×#6732 | C2 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
706 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240784);