#24987739

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

C₄₃ ⋊ #8263

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₃
commutator, socle, prime radical	C₂³×C₄₃	C₂×C₄²
Fitting	C₄×C₄⋊C₈×C₄₃	C₂
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₄×C₄⋊C₈	D₄₃
hypocenter	C₄₃	#8263
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ C₄×C₄⋊C₈

470 conjugacy classes of subgroups.

Polycyclic presentation:

2^8,43|a^2=e,b^2=f,c^2=de,e^2=g,f^2=h,b^a=bd,c^a=cg,i^a=i^42,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, 60710);