#32204176

order	18176
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁷

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₁
commutator, socle, prime radical, cosocle	C₂³×C₇₁	C₂⁵
Frattini	C₂³	C₂⁴×D₇₁
Fitting	C₄×#125×C₇₁	C₂
hypercenter	C₄×#125	D₇₁
hypocenter	C₇₁	#36701
LCS	G ▷ C₂³×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#125

1304 conjugacy classes of subgroups.

μ_t(G) = 18176

Polycyclic presentation:

2^8,71|a^2=h,b^2=h,c^2=f,d^2=f,e^2=g,b^a=bf,c^a=cg,d^a=dh,c^b=ch,d^c=dfh,i^c=i^70

2012 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 376292);