#25016368

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

Aliases

No aliases for this group.

Splittings

Sylow

C₄₃ ⋊ #13477

Subgroups

	subgroup	G/H
center	C₂³	C₂×#10621882
commutator, cosocle	C₂²×C₈×C₄₃	C₂³
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1942	C₂
socle, prime radical	C₂³×C₄₃	C₂×D₈
hypercenter	#1942	D₄₃
hypocenter	C₄₃	#13477
LCS	G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1942

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=de,b^2=dgh,c^2=h,d^2=gh,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fgh,g^a=gh,c^b=cf,i^b=i^42,d^c=dg,e^c=egh,f^c=fgh,g^c=gh,i^c=i^42

Conjugacy classes & character table

976 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 89339);