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#431×C₁₃₉ #22580516

order	8896
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

#431×C₁₃₉

Subgroups

	subgroup	G/H
center	C₄²×C₁₃₉	C₂²
commutator	C₂	C₂²×C₈×C₁₃₉
Frattini, cosocle	C₂×C₄	C₂³×C₁₃₉
socle	C₂²×C₁₃₉	C₂²×C₄
prime radical	C₂³×C₁₃₉	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃₉ ◁ G

118 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	#31804232, #31804234, #31804236, …
maximal subgroup of	#1274×C₁₃₉, #1275×C₁₃₉, #1276×C₁₃₉, …
maximal normal subgroup of	#1274×C₁₃₉, #1275×C₁₃₉, #1276×C₁₃₉, …
maximal quotient of	#1744×C₁₃₉, C₄×C₂²⋊C₈×C₁₃₉, C₄×C₄⋊C₈×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 112);