Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of SL(2,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C4×SL(2,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C22×C4 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C4 |
| Frattini, cosocle | C22 | C22×A5 |
| socle | C23 | C2×A5 |
| prime radical | C22×SL(2,𝔽5) | C2 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22×C4 | |
197 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#91143, #14514921, C42×SL(2,𝔽5), … |
| maximal normal subgroup of | C4×#91143, #14514921, C42×SL(2,𝔽5), … |
| maximal quotient of | C42×SL(2,𝔽5), C22⋊C4×SL(2,𝔽5), C4⋊C4×SL(2,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5745);