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#376×C₁₄₉ #23749133

order	9536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₄₉ · Schur multiplier (H₂) = C₂×C₄²

Aliases

#376×C₁₄₉

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	C₂²
commutator	C₂	C₂×C₄²×C₁₄₉
Frattini, cosocle	C₂³	C₂³×C₁₄₉
socle, prime radical	C₂³×C₁₄₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ G

178 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	#34042520, #34042584, #34043175, …
maximal subgroup of	#1274×C₁₄₉, #1300×C₁₄₉, #1500×C₁₄₉, …
maximal normal subgroup of	#1274×C₁₄₉, #1300×C₁₄₉, #1500×C₁₄₉, …
maximal quotient of	C₄×#95×C₁₄₉, #1434×C₁₄₉, #1744×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 57);