Finite Group Databasebeta

← Prev (#22580421) Next (#22580423) →

H(3,ℤ/4)×C₁₃₉ #22580422

order	8896
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₃₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

H(3,ℤ/4)×C₁₃₉

Subgroups

	subgroup	G/H
center	C₄×C₁₃₉	C₄²
commutator	C₄	C₄²×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂²×C₁₃₉
socle	C₂×C₁₃₉	#95
prime radical	C₂³×C₁₃₉	D₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₉ ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3058 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31804388, #31804391, H(3,ℤ/4)×D₁₃₉, …
maximal subgroup of	#1339×C₁₃₉, #1340×C₁₃₉, C₂×H(3,ℤ/4)×C₁₃₉, …
maximal normal subgroup of	#1339×C₁₃₉, #1340×C₁₃₉, C₂×H(3,ℤ/4)×C₁₃₉, …
maximal quotient of	#1274×C₁₃₉, #1275×C₁₃₉, #1284×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 18);