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#504×C₁₄₉ #23749261

order	9536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₄₉ · Schur multiplier (H₂) = C₂²

Aliases

#504×C₁₄₉

Subgroups

	subgroup	G/H
center	C₁₆×C₁₄₉	C₂²
commutator	C₂	C₂²×C₈×C₁₄₉
Frattini, cosocle	C₈	C₂³×C₁₄₉
socle	C₂×C₁₄₉	C₂²×C₈
prime radical	#41×C₁₄₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₄₉ ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5960 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#34042833, #34046526, #34046531, …
maximal subgroup of	#1401×C₁₄₉, #2170×C₁₄₉, #2171×C₁₄₉, …
maximal normal subgroup of	#1401×C₁₄₉, #2170×C₁₄₉, #2171×C₁₄₉, …
maximal quotient of	#2108×C₁₄₉, #2113×C₁₄₉, #2151×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 185);