Finite Group Databasebeta

← Prev (#19149556) Next (#19149558) →

#117×C₁₇₃ #19149557

order	5536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

#117×C₁₇₃

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇₃	C₂²
commutator	C₂	C₂²×C₄×C₁₇₃
Frattini, cosocle	C₂²	C₂³×C₁₇₃
socle	C₂²×C₁₇₃	C₂³
prime radical	C₂³×C₁₇₃	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇₃ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3460 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36368501, #36368511, #36368613, …
maximal subgroup of	H(3,ℤ/4)×C₁₇₃, #339×C₁₇₃, #344×C₁₇₃, …
maximal normal subgroup of	H(3,ℤ/4)×C₁₇₃, #339×C₁₇₃, #344×C₁₇₃, …
maximal quotient of	#376×C₁₇₃, C₄×C₂²⋊C₄×C₁₇₃, C₄×C₄⋊C₄×C₁₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5536, 24);