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#322×C₁₄₉ #23749079

order	9536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₄₉ · Schur multiplier (H₂) = C₄

Aliases

#322×C₁₄₉

Subgroups

	subgroup	G/H
center	C₄²×C₁₄₉	C₂²
commutator	C₂	C₄×C₈×C₁₄₉
Frattini, cosocle	C₄²	C₂²×C₁₄₉
socle, prime radical	C₂²×C₁₄₉	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₄₉ ◁ G

66 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	#34042612, #34042668, #322×D₁₄₉, …
maximal subgroup of	#1313×C₁₄₉, #1336×C₁₄₉, C₂×#322×C₁₄₉, …
maximal normal subgroup of	#1313×C₁₄₉, #1336×C₁₄₉, C₂×#322×C₁₄₉, …
maximal quotient of	#1273×C₁₄₉, #1312×C₁₄₉, #1313×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 3);