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#322×C₁₃₉ #22580407

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

Aliases

#322×C₁₃₉

Subgroups

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

66 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	#31804325, #31804381, #322×D₁₃₉, …
maximal subgroup of	#1313×C₁₃₉, #1336×C₁₃₉, C₂×#322×C₁₃₉, …
maximal normal subgroup of	#1313×C₁₃₉, #1336×C₁₃₉, C₂×#322×C₁₃₉, …
maximal quotient of	#1273×C₁₃₉, #1312×C₁₃₉, #1313×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 3);