Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of SL(2,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×#6732 |
| derived | SL(2,𝔽5) ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C4×C8 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C8 |
| Frattini, cosocle | C2×C4 | C22×A5 |
| socle | C22 | C2×C4×A5 |
| prime radical | C2×#6732 | C4 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C4×C8 | |
282 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#6732, #72276979, C8×GL(2,𝔽5) |
| maximal normal subgroup of | SD16×#6732, #72276979, C8×GL(2,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240687);