C₂²⋊AΓL(1,𝔽₈) #10621675

order	672
isoclinism	isoclinic class of C₂²⋊AΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	C₂²⋊AΓL(1,𝔽₈)
unambiguous semidirect product	AGL(1,𝔽₈)⋊A₄

Fitting, socle, Sylow	C₂⁵ ⋊ ΓL(1,𝔽₈)
derived, Hall	C₂²×AGL(1,𝔽₈) ⋊ C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂²×AGL(1,𝔽₈)	C₃
Fitting, socle	C₂⁵	ΓL(1,𝔽₈)
LCS	G ▷ C₂²×AGL(1,𝔽₈)
UCS	C₁

54 conjugacy classes of subgroups.

μ_t(G) = 28

Polycyclic presentation:

3,2^2,7,2^3|b^a=c,c^a=bc,d^a=d^2,f^a=g,g^a=efg,e^d=f,f^d=g,g^d=eg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 1257);