ΓL(1,𝔽₈)⋊#1035 #14523535

order	2100
isoclinism	isoclinic class of ΓL(1,𝔽₈)⋊#1035
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	ΓL(1,𝔽₈)⋊#1035
unambiguous semidirect product	(C₇⋊#1035)⋊C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₇×C₂₅	C₃×C₄
Frattini	C₅	ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)
socle	C₅×C₇	C₃×AGL(1,𝔽₅)
prime radical	ΓL(1,𝔽₈)×D₂₅	C₂
cosocle	C₇×D₂₅	C₂×C₃
LCS	G ▷ C₇×C₂₅
UCS	C₁

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 175

Polycyclic presentation:

2,3,2,5,7,5|a^2=c,d^5=f^2,d^a=d^3f,e^a=e^6,f^a=f^3,e^b=e^2,d^c=d^4f^3,f^c=f^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 15);