Finite Group Databasebeta

← Prev (#22580414) Next (#22580416) →

#330×C₁₃₉ #22580415

order	8896
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃₉ · Schur multiplier (H₂) = C₁

Aliases

#330×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

60 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	#330×D₁₃₉, #31804991, #31804997, …
maximal subgroup of	C₂×#330×C₁₃₉, #1524×C₁₃₉, #1526×C₁₃₉, …
maximal normal subgroup of	C₂×#330×C₁₃₉, #1524×C₁₃₉, #1526×C₁₃₉, …
maximal quotient of	#1271×C₁₃₉, #1295×C₁₃₉, C₂×#330×C₁₃₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 11);