Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of C3⋊ΓL(2,𝔽4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C3⋊ΓL(2,𝔽4) |
| unambiguous semidirect product | A5⋊(C3⋊D3) |
| Fitting | C32 ⋊ S5 |
| socle, derived | C32×A5 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, cosocle, hypocenter | C32×A5 | C2 |
| Fitting | C32 | S5 |
| LCS | G ▷ C32×A5 | |
| UCS | C1 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
Permutation generators:
(1,4,2)(3,5)(6,7)(10,11);(1,2,5,3)(7,8)(9,10);(1,3,5,4)(6,7)(9,11)27 conjugacy classes — view the full character table.
| maximal subgroup of | #72241556, D3×ΓL(2,𝔽4), #72247634, … |
| maximal normal subgroup of | D3×ΓL(2,𝔽4), C3⋊D3×S5 |
| maximal quotient of | #72241556, #72247634 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 488);