(C₄³⋊C₇)⋊C₃ #13051526

order	1344
isoclinism	isoclinic class of (C₄³⋊C₇)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₁

Aliases

(C₄³⋊C₇)⋊C₃

Fitting, Sylow	C₄³ ⋊ ΓL(1,𝔽₈)
derived, Hall	C₄³⋊C₇ ⋊ C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₄³⋊C₇	C₃
Frattini, socle	C₂³	AΓL(1,𝔽₈)
Fitting	C₄³	ΓL(1,𝔽₈)
LCS	G ▷ C₄³⋊C₇
UCS	C₁

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 28

Polycyclic presentation:

3,7,2^6|c^2=g,d^2=h,e^2=f,b^a=b^2,c^a=cd,d^a=ch,e^a=egh,g^a=gh,h^a=g,c^b=de,d^b=cg,e^b=df,f^b=h,g^b=fh,h^b=g

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 815);