#87656⋊C₂ #11716141

order	784
isoclinism	isoclinic class of #87656⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	#87656⋊C₂
unambiguous semidirect product	(#5997⋊C₂)⋊C₂

C₇² ⋊ D₈

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	#5997	C₂²
Fitting, socle, hypocenter	C₇²	D₈
LCS	G ▷ #5997 ▷ C₇⋊D₇ ▷ C₇²
UCS	C₁

32 conjugacy classes of subgroups.

μ_t(G) = 28

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(784, 161);