#13056615

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₂₁
commutator, socle, prime radical, cosocle	C₂³×C₃×C₇	C₂³
Fitting	C₂×C₃×C₇×C₄⋊C₄	C₂
hypercenter	C₂×C₄⋊C₄	D₂₁
hypocenter	C₃×C₇	#398
LCS	G ▷ C₂³×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 1344

Polycyclic presentation:

2^6,3,7|a^2=f,b^2=f,c^2=f,b^a=be,c^a=cef,g^a=g^2,h^a=h^6,c^b=cd

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5904);