Finite Group Databasebeta

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C₈×#13063349 #25066006

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

C₈×#13063349

Splittings

Fitting	C₈×D₈×C₄₃ ⋊ C₂
Sylow	C₄₃ ⋊ C₈×AGL(1,ℤ/8)

Subgroups

	subgroup	G/H
center	C₂×C₈	D₄×D₄₃
commutator	C₄×C₄₃	C₂³×C₈
Frattini	C₄²	C₂³×D₄₃
Fitting	C₈×D₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063349	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₈×D₈	D₄₃
hypocenter	C₄₃	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×D₈

802 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 138977);