ΓL(1,𝔽₈)⋊C₃₂ #10620419

order	672
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₂ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	ΓL(1,𝔽₈)⋊C₃₂
unambiguous semidirect product	(C₇⋊C₃₂)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₃×C₃₂
Fitting, cosocle	C₇×C₁₆	C₂×C₃
socle	C₂×C₇	C₃×C₁₆
prime radical	C₂×ΓL(1,𝔽₈)	C₁₆
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₆

24 conjugacy classes of subgroups.

μ_t(G) = 224

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 1);