Finite Group Databasebeta

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#333×C₁₃₉ #22580418

order	8896
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂

Aliases

#333×C₁₃₉

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2641 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31804559, #333×D₁₃₉, #31805058, …
maximal subgroup of	#1405×C₁₃₉, C₂×#333×C₁₃₉, #1542×C₁₃₉, …
maximal normal subgroup of	#1405×C₁₃₉, C₂×#333×C₁₃₉, #1542×C₁₃₉, …
maximal quotient of	#1272×C₁₃₉, #1296×C₁₃₉, #1366×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 14);