Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#91145 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×A5 |
| commutator, hypocenter | C3×SL(2,𝔽5) | C4 |
| Fitting, cosocle | C3×C4 | C2×A5 |
| socle | C2×C3 | C4×A5 |
| prime radical | C3×#6732 | C2 |
| LCS | G ▷ C3×SL(2,𝔽5) | |
| UCS | C1 ◁ C4 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Permutation generators:
(1,2,8,16,4,6,11,26,43,18,22,35,45,21,38,44,25,20,5,19,37,48,31,14,40,42,28,9,17,41,23,36,30,39,15,7,12,27,13,3)(10,24,29,34,47,33,46,32)(50,51);(1,4,17,22,38,13,37,40,43,23,15,5)(2,9,29,35,27,47,48,26,46,36,20,10)(3,14,6,18,39,44,19,16,42,41,21,7)(8,24,28,45,34,12,31,33,11,30,32,25)(49,50,51)54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1689);