AΓL(1,𝔽₂₅) #11925736

order	1200
isoclinism	isoclinic class of AΓL(1,𝔽₂₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₁

Aliases

affine general semilinear	AΓL(1,𝔽₂₅)
unambiguous semidirect product	#10597167⋊C₂
unambiguous semidirect product	AGL(1,𝔽₂₅)⋊C₂

Fitting, socle, Sylow	C₅² ⋊ ΓL(1,𝔽₂₅)
Hall	C₅²⋊C₃ ⋊ M₁₆

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator	(C₅⋊D₅)⋊C₃	C₂×C₄
Fitting, socle	C₅²	ΓL(1,𝔽₂₅)
prime radical	#3874⋊C₂	C₄
cosocle	#1043⋊C₃	C₂²
hypocenter	C₅²⋊C₃	M₁₆
LCS	G ▷ (C₅⋊D₅)⋊C₃ ▷ C₅²⋊C₃
UCS	C₁

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 25

Polycyclic presentation:

2^4,3,5^2|a^2=c,c^2=d,b^a=bd,f^a=f^4g,g^a=f^2g,e^b=e^2,g^b=f^2g^4,f^c=f^3,g^c=g^3,f^d=f^4,g^d=g^4,f^e=fg,g^e=f^2g^3

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 946);