Finite Group Databasebeta

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#443×C₁₃₉ #22580528

order	8896
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂²

Aliases

#443×C₁₃₉

Subgroups

	subgroup	G/H
center	C₈×C₁₃₉	D₄
commutator	C₄	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂×C₄	C₂³×C₁₃₉
socle	C₂×C₁₃₉	C₄×D₄
prime radical	#135×C₁₃₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃₉ ◁ C₂×C₈×C₁₃₉ ◁ G

106 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3892 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31804377, #31804380, #31808241, …
maximal subgroup of	#1335×C₁₃₉, #1336×C₁₃₉, #2170×C₁₃₉, …
maximal normal subgroup of	#1335×C₁₃₉, #1336×C₁₃₉, #2170×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, 124);