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#376×C₁₃₉ #22580461

order	8896
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₃₉ · Schur multiplier (H₂) = C₂×C₄²

Aliases

#376×C₁₃₉

Subgroups

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

178 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	#31804233, #31804297, #31804888, …
maximal subgroup of	#1274×C₁₃₉, #1300×C₁₃₉, #1500×C₁₃₉, …
maximal normal subgroup of	#1274×C₁₃₉, #1300×C₁₃₉, #1500×C₁₃₉, …
maximal quotient of	C₄×#95×C₁₃₉, #1434×C₁₃₉, #1744×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 57);