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C₈×D₄×C₁₃₉ #22580519

order	8896
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃₉ · Schur multiplier (H₂) = C₂³

Aliases

C₈×D₄×C₁₃₉

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₃₉	C₂²
commutator	C₂	C₂²×C₈×C₁₃₉
Frattini, cosocle	C₂×C₄	C₂³×C₁₃₉
socle	C₂²×C₁₃₉	C₂²×C₄
prime radical	C₂×D₄×C₁₃₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₉ ◁ G

134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5560 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	D₄⋊(C₁₃₉⋊C₁₆), C₈×#14555770, C₈×#14555773, …
maximal subgroup of	D₄⋊C₁₆×C₁₃₉, C₈×D₈×C₁₃₉, C₈×SD₁₆×C₁₃₉, …
maximal normal subgroup of	D₄⋊C₁₆×C₁₃₉, C₈×D₈×C₁₃₉, C₈×SD₁₆×C₁₃₉, …
maximal quotient of	C₈×D₈×C₁₃₉, C₈×SD₁₆×C₁₃₉, C₈×Q₁₆×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 115);