Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C5⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×A4⋊Dic5 |
| unambiguous semidirect product | A4⋊(C5×Dic5) |
| derived | C5×A4 ⋊ C4×C5 |
| Sylow | C52 ⋊ SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C5⋊S4 |
| commutator, hypocenter | C5×A4 | C4×C5 |
| Frattini | C2 | C5×C5⋊S4 |
| Fitting, socle | C23×C52 | D3 |
| prime radical | C2×C52×A4 | C2 |
| cosocle | C2×C5×A4 | C2×C5 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C2×C5 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#91958, #72260291, #72260292, … |
| maximal normal subgroup of | C5×#91958, #72260291, #72260292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 676);