#37535626

order	23168
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₁₈₁ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₈₁
commutator, socle, prime radical	C₂²×C₁₈₁	C₂²×C₈
Fitting	C₄⋊C₁₆×C₁₈₁	C₂
cosocle	C₂×C₈×C₁₈₁	C₂³
hypercenter	C₄⋊C₁₆	D₁₈₁
hypocenter	C₁₈₁	#2183
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

126 conjugacy classes of subgroups.

μ_t(G) = 23168

Polycyclic presentation:

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

3656 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 6415);