Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of A4⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | A4⋊#1035 |
| Fitting | C22×C25 ⋊ Dic3 |
| derived | A4×C25 ⋊ C4 |
| Sylow | C25 ⋊ SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | A4×C25 | C4 |
| Frattini | C5 | A4⋊AGL(1,𝔽5) |
| Fitting | C22×C25 | Dic3 |
| socle | C22×C5 | ΓL(1,𝔽16) |
| prime radical, cosocle | A4×D25 | C2 |
| LCS | G ▷ A4×C25 | |
| UCS | C1 | |
57 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 100 |
Polycyclic presentation:
2^2,3,5^2,2^2|a^2=b,d^5=e,c^a=c^2,d^a=d^2e,e^a=e^2,f^a=fg,d^b=d^4e^4,e^b=e^4,f^c=g,g^c=fg34 conjugacy classes — view the full character table.
| maximal subgroup of | #72228881, S4×#1035 |
| maximal normal subgroup of | #72228881, S4×#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 193);