#25014216

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₄₃
commutator, socle, prime radical	C₂³×C₄₃	C₂²×C₈
Fitting	C₂×C₄₃×C₄⋊C₁₆	C₂
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₄₃
hypocenter	C₄₃	#13105
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

314 conjugacy classes of subgroups.

Polycyclic presentation:

2^8,43|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^42

1768 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 87187);