Finite Group Databasebeta

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#350×C₁₃₉ #22580435

order	8896
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃₉ · Schur multiplier (H₂) = C₂

Aliases

#350×C₁₃₉

Subgroups

	subgroup	G/H
center	C₈×C₁₃₉	D₄
commutator	C₄	C₂×C₈×C₁₃₉
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₉
socle	C₂×C₁₃₉	C₂²⋊C₈
prime radical	#41×C₁₃₉	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃₉ ◁ C₂×C₈×C₁₃₉ ◁ G

56 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	#350×D₁₃₉, #31808030, #31808238, …
maximal subgroup of	C₂×#350×C₁₃₉, #2117×C₁₃₉, #2170×C₁₃₉, …
maximal normal subgroup of	C₂×#350×C₁₃₉, #2117×C₁₃₉, #2170×C₁₃₉, …
maximal quotient of	#1315×C₁₃₉, #1323×C₁₃₉, D₄⋊C₁₆×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 31);