Finite Group Databasebeta

← Prev (#22552791) Next (#22552793) →

C₂²⋊C₁₆×C₁₃₁ #22552792

order	8384
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₃₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂²⋊C₁₆×C₁₃₁
unambiguous semidirect product	C₂²⋊(C₁₆×C₁₃₁)

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₃₁	C₂²
commutator	C₂	C₂×C₁₆×C₁₃₁
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₁
socle	C₂²×C₁₃₁	C₂×C₈
prime radical	C₂³×C₁₃₁	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₁ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5240 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30663884, #30663886, #30663900, …
maximal subgroup of	#1314×C₁₃₁, #1315×C₁₃₁, #1322×C₁₃₁, …
maximal normal subgroup of	#1314×C₁₃₁, #1315×C₁₃₁, #1322×C₁₃₁, …
maximal quotient of	#1314×C₁₃₁, #1322×C₁₃₁, D₄⋊C₁₆×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 29);