#13057159

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²	C₂×C₇⋊S₄
commutator, prime radical, cosocle	C₂×C₇×SL(2,𝔽₃)	C₂²
Fitting	C₄×C₇×Q₈	D₃
socle	C₂²×C₇	C₂×S₄
hypercenter	C₂×C₄	C₇⋊S₄
hypocenter	C₇×SL(2,𝔽₃)	Q₈
LCS	G ▷ C₂×C₇×SL(2,𝔽₃) ▷ C₇×SL(2,𝔽₃)
UCS	C₁ ◁ C₂² ◁ C₂×C₄

118 conjugacy classes of subgroups.

μ_t(G) = 448

Polycyclic presentation:

2^3,3,7,2^3|a^2=c,b^2=ch,f^2=h,g^2=h,b^a=bch,d^a=d^2,e^a=e^6,f^a=fg,g^a=gh,f^d=g,g^d=fgh,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 6448);