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C₈×D₄×C₁₄₉ #23749191

order	9536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₄₉ · Schur multiplier (H₂) = C₂³

Aliases

C₈×D₄×C₁₄₉

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₄₉	C₂²
commutator	C₂	C₂²×C₈×C₁₄₉
Frattini, cosocle	C₂×C₄	C₂³×C₁₄₉
socle	C₂²×C₁₄₉	C₂²×C₄
prime radical	C₂×D₄×C₁₄₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₄₉ ◁ G

134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5960 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	D₄⋊#14558711, C₈×#14558721, C₈×#14558724, …
maximal subgroup of	D₄⋊C₁₆×C₁₄₉, C₈×D₈×C₁₄₉, C₈×SD₁₆×C₁₄₉, …
maximal normal subgroup of	D₄⋊C₁₆×C₁₄₉, C₈×D₈×C₁₄₉, C₈×SD₁₆×C₁₄₉, …
maximal quotient of	C₈×D₈×C₁₄₉, C₈×SD₁₆×C₁₄₉, C₈×Q₁₆×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 115);