#30669269

order	16768
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₃₁ ⋊ #2402

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₃₁
commutator, socle, prime radical, cosocle	C₂³×C₁₃₁	C₂⁴
Frattini	C₂³	C₂³×D₁₃₁
Fitting	C₄×C₄⋊C₄×C₁₃₁	C₂
hypercenter	C₄×C₄⋊C₄	D₁₃₁
hypocenter	C₁₃₁	#2402
LCS	G ▷ C₂³×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

400 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.

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

μ_t(G) = 16768

Polycyclic presentation:

2^7,131|a^2=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^130,c^b=cg,h^b=h^130

2644 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16768, 7818);