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#24997865

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

Splittings

C₄₃ ⋊ #10076

Subgroups

	subgroup	G/H
center	C₂³	#13063295
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×D₄⋊C₈	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₄×C₄₃	D₄
hypercenter	C₂×D₄⋊C₈	D₄₃
hypocenter	C₄₃	#10076
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×D₄⋊C₈

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=gh,b^2=gh,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^42,c^b=cf,d^b=dg,e^b=eh,i^b=i^42,d^c=dh,e^c=eh

Conjugacy classes & character table

1222 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 70836);