Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C4⋊ΓL(2,𝔽4) |
| Fitting | C3×C4 ⋊ S5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×ΓL(2,𝔽4) |
| commutator, socle, cosocle | C2×C3×A5 | C22 |
| Fitting | C3×C4 | S5 |
| hypercenter | C4 | ΓL(2,𝔽4) |
| hypocenter | C3×A5 | D4 |
| LCS | G ▷ C2×C3×A5 ▷ C3×A5 | |
| UCS | C1 ◁ C2 ◁ C4 | |
216 conjugacy classes of subgroups; only the 15 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 15 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
Permutation generators:
(1,5,4,2)(7,8)(10,11);(1,5,3)(6,8,9,7)(10,11,12)39 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4630);