#13052307

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₃×D₇
commutator, socle, prime radical	C₂²×C₃×C₇	C₂²×C₄
Fitting	C₃×C₄²×C₇	C₂²
cosocle	C₂×C₃×C₄×C₇	C₂³
hypercenter	C₄²	D₃×D₇
hypocenter	C₃×C₇	#446
LCS	G ▷ C₂²×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

188 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 92 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=e,b^2=d,c^2=e,d^2=f,b^a=be,c^a=cef,h^a=h^6,g^b=g^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 1596);