Finite Group Databasebeta

← Prev (#22580448) Next (#22580450) →

#364×C₁₃₉ #22580449

order	8896
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃₉ · Schur multiplier (H₂) = C₁

Aliases

#364×C₁₃₉

Subgroups

	subgroup	G/H
center	C₈×C₁₃₉	D₄
commutator	C₄	C₂×C₈×C₁₃₉
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₉
socle	C₂×C₁₃₉	C₄⋊C₈
prime radical	C₂²×C₁₃₉	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃₉ ◁ C₂×C₈×C₁₃₉ ◁ G

46 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	#31804376, #31804379, #31804440, …
maximal subgroup of	#1335×C₁₃₉, #1336×C₁₃₉, #1357×C₁₃₉, …
maximal normal subgroup of	#1335×C₁₃₉, #1336×C₁₃₉, #1357×C₁₃₉, …
maximal quotient of	#1367×C₁₃₉, #1370×C₁₃₉, #1376×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 45);