#32016383

order	18176
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₁
commutator, socle, prime radical	C₂³×C₇₁	C₂³×C₄
Fitting	C₇₁×#1939	C₂
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	#1939	D₇₁
hypocenter	C₇₁	#22737
LCS	G ▷ C₂³×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

712 conjugacy classes of subgroups.

μ_t(G) = 18176

Polycyclic presentation:

2^8,71|a^2=g,b^2=e,c^2=ef,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=dh,c^b=ch,d^b=de,i^b=i^70,i^c=i^70,i^d=i^70

2024 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 188499);