C₇⋊#4621 #13051538

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₂	C₇⋊#857
commutator, prime radical, cosocle, hypocenter	C₇×#95⋊C₃	C₂
Frattini	C₂³	C₇⋊S₄
Fitting	C₇×#95	D₃
socle	C₂³×C₇	S₄
LCS	G ▷ C₇×#95⋊C₃
UCS	C₁ ◁ C₂

74 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 168

Polycyclic presentation:

2,3,7,2^5|a^2=fg,d^2=f,e^2=fgh,b^a=b^2,c^a=c^6,d^a=deh,e^a=efgh,f^a=fh,g^a=gh,d^b=eg,e^b=defg,f^b=fgh,g^b=h,h^b=gh,e^d=efg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 827);