#25101294

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle, prime radical	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1746	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1746	D₄₃
hypocenter	C₄₃	#21341
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1746

686 conjugacy classes of subgroups.

Polycyclic presentation:

2^8,43|a^2=g,b^2=fg,c^2=f,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=dh,i^c=i^42

1264 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 174265);