Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of ΓL(2,𝔽4) |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C3⋊(A5⋊C8) |
| unambiguous semidirect product | A5⋊(C3⋊C8) |
| derived | C3×A5 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | ΓL(2,𝔽4) |
| commutator, hypocenter | C3×A5 | C8 |
| Fitting | C3×C4 | S5 |
| socle, prime radical | C2×C3×A5 | C4 |
| cosocle | C3×C4×A5 | C2 |
| LCS | G ▷ C3×A5 | |
| UCS | C1 ◁ C4 | |
108 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 13 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Permutation generators:
(1,2)(3,4)(5,6)(7,8)(9,11,13,12,10)(14,16,15);(1,8,6,4,2,7,5,3)(9,13,11)(10,12)(15,16)48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1685);