#32028442

order	18176
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

	subgroup	G/H
center	C₄	C₇₁⋊#401
commutator, prime radical, cosocle	C₂⁴×C₇₁	C₂⁴
Frattini	C₂⁴	C₂³×D₇₁
Fitting	C₇₁×#1740	C₂
socle	C₂×C₇₁	C₂×#401
hypercenter	#1740	D₇₁
hypocenter	C₇₁	#23847
LCS	G ▷ C₂⁴×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1740

604 conjugacy classes of subgroups.

μ_t(G) = 2272

Polycyclic presentation:

2^8,71|a^2=efg,b^2=ef,c^2=e,d^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,c^b=cg,g^b=gh,f^c=fh,i^c=i^70

1586 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 200558);