Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of (C5⋊D5)⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | #1039⋊A4 |
| derived | C22×C52 ⋊ C3×C4 |
| Hall | C22×#1039 ⋊ C3 |
| Sylow | C52 ⋊ C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C5⋊D5)⋊A4 |
| commutator, hypocenter | C22×C52 | C3×C4 |
| Fitting, socle, cosocle | C23×C52 | C2×C3 |
| prime radical | C2×C22⋊(C52⋊C3) | C2 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C2 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2,3,2^3,5^2|a^2=c,f^a=f^4,g^a=g^4,d^b=de,e^b=d,f^b=fg^3,g^b=f^4g^348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 701);