C₇⋊#1043 #10622002

order	700
isoclinism	isoclinic class of C₇⋊#1043
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₇	C₄
prime radical, cosocle	C₇×C₅⋊D₅	C₂
LCS	G ▷ C₅²×C₇
UCS	C₁

48 conjugacy classes of subgroups.

μ_t(G) = 175

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(700, 21);