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×GL(2,𝔽5) |
| derived | SL(2,𝔽5) ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C4 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C3×C4 |
| Frattini | C4 | C3×S5 |
| socle | C2×C3 | A5⋊C4 |
| prime radical | C3×#6732 | C2 |
| cosocle | #6732 | C2×C3 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C3×C4 | |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1683);