Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C5⋊S5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | A5⋊Dic5 |
| derived | C5×A5 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊S5 |
| commutator, hypocenter | C5×A5 | C4 |
| Fitting | C2×C5 | S5 |
| socle, prime radical, cosocle | C2×C5×A5 | C2 |
| LCS | G ▷ C5×A5 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
Permutation generators:
(1,2)(3,5)(6,7)(8,9,10)(11,13,12,14);(1,3)(2,4)(6,9,10)(7,8)(11,14,12,13)34 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A5⋊Dic5, C2×A5⋊Dic5, D5×A5⋊C4 |
| maximal normal subgroup of | C3×A5⋊Dic5, C2×A5⋊Dic5, D5×A5⋊C4 |
| maximal quotient of | #72219146, C3×A5⋊Dic5, C2×A5⋊Dic5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 476);