Finite Group Databasebeta

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#504×C₁₃₇ #22577039

order	8768
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃₇ · Schur multiplier (H₂) = C₂²

Aliases

#504×C₁₃₇

Subgroups

	subgroup	G/H
center	C₁₆×C₁₃₇	C₂²
commutator	C₂	C₂²×C₈×C₁₃₇
Frattini, cosocle	C₈	C₂³×C₁₃₇
socle	C₂×C₁₃₇	C₂²×C₈
prime radical	#41×C₁₃₇	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₃₇ ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5480 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31778931, #31782624, #31782629, …
maximal subgroup of	#1401×C₁₃₇, #2170×C₁₃₇, #2171×C₁₃₇, …
maximal normal subgroup of	#1401×C₁₃₇, #2170×C₁₃₇, #2171×C₁₃₇, …
maximal quotient of	#2108×C₁₃₇, #2113×C₁₃₇, #2151×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 185);