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#25132894

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Splittings

C₄₃ ⋊ #24320

Subgroups

	subgroup	G/H
center	C₂²	C₂×#13063293
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×AGL(1,ℤ/8)×C₄₃	C₂
socle	C₂²×C₄₃	C₂×#120
prime radical	C₂×AGL(1,ℤ/8)×C₄₃	C₂²
hypercenter	C₄×AGL(1,ℤ/8)	D₄₃
hypocenter	C₄₃	#24320
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

1092 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=e,b^2=e,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^42,c^b=cg,g^b=gh,f^c=fh,g^c=gh

Conjugacy classes & character table

967 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 205865);