A₄⋊D₂₅ #10597054

order	600
isoclinism	isoclinic class of A₄⋊D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	A₄⋊D₂₅
unambiguous semidirect product	C₂₅⋊S₄

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	A₄×C₂₅	C₂
Frattini	C₅	C₅⋊S₄
Fitting	C₂²×C₂₅	D₃
socle	C₂²×C₅	D₁₅
LCS	G ▷ A₄×C₂₅
UCS	C₁

33 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 100

Polycyclic presentation:

2,3,5^2,2^2|c^5=d^4,b^a=b^2,c^a=c^4d,d^a=d^4,e^a=f,f^a=e,e^b=f,f^b=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(600, 35);