Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #6728 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#91143 |
| derived | SL(2,𝔽5) ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C22×C3 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C3×C4 |
| Frattini | C22 | C3×S5 |
| prime radical | C2×C3×SL(2,𝔽5) | C2 |
| cosocle | C2×SL(2,𝔽5) | C2×C3 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22×C3 | |
104 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1684);