#37541990

order	23168
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₈₁ ⋊ #2843

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₈₁
commutator, socle, prime radical, cosocle	C₂³×C₁₈₁	C₂⁴
Fitting	#384×C₁₈₁	C₂
hypercenter	#384	D₁₈₁
hypocenter	C₁₈₁	#2843
LCS	G ▷ C₂³×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂³ ◁ #384

348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

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

μ_t(G) = 23168

Polycyclic presentation:

2^7,181|a^2=f,b^2=g,c^2=g,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,h^b=h^180,d^c=de

2546 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 12779);