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Q₈×#13063349 #25977167

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁸

Aliases

Q₈×#13063349

Splittings

Fitting	Q₈×D₈×C₄₃ ⋊ C₂
Sylow	C₄₃ ⋊ Q₈×AGL(1,ℤ/8)

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	Q₈×D₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂×#13063349	C₂²
hypercenter	Q₈×D₈	D₄₃
hypocenter	C₄₃	Q₈×AGL(1,ℤ/8)
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ Q₈×D₈

2010 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

790 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1050138);