#13094367

order	1512
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₇×C₃⋊D₃
commutator, Fitting, prime radical, cosocle	C₂×C₇×H(3,𝔽₃)	C₂²
socle	C₂×C₃×C₇	C₂×C₃⋊D₃
hypocenter	C₇×H(3,𝔽₃)	Q₈
LCS	G ▷ C₂×C₇×H(3,𝔽₃) ▷ C₇×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

132 conjugacy classes of subgroups.

μ_t(G) = 504

Polycyclic presentation:

2^3,3^2,7,3|a^2=c,b^2=c,b^a=bc,f^a=f^6,d^b=d^2,e^b=e^2,e^d=eg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 264);