Finite Group Databasebeta

← Prev (#22580468) Next (#22580470) →

#384×C₁₃₉ #22580469

order	8896
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

#384×C₁₃₉

Subgroups

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

186 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	#31804287, #31804350, #31806401, …
maximal subgroup of	#1296×C₁₃₉, #1325×C₁₃₉, #1802×C₁₃₉, …
maximal normal subgroup of	#1296×C₁₃₉, #1325×C₁₃₉, #1802×C₁₃₉, …
maximal quotient of	C₄⋊#95×C₁₃₉, #1444×C₁₃₉, #1842×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 65);