#31915071

order	18176
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₇₁
commutator, socle, prime radical	C₂³×C₇₁	C₂²×C₈
Fitting	C₂×C₄⋊C₁₆×C₇₁	C₂
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₇₁
hypocenter	C₇₁	#13105
LCS	G ▷ C₂³×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

314 conjugacy classes of subgroups.

μ_t(G) = 18176

Polycyclic presentation:

2^8,71|a^2=f,b^2=f,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,c^b=ch,i^c=i^70

2888 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 87187);