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C₂²×C₂²⋊C₄×C₁₄₉ #23749269

order	9536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₄₉ · Schur multiplier (H₂) = C₂⁷

Aliases

C₂²×C₂²⋊C₄×C₁₄₉

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₄₉	C₂²
commutator	C₂	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²	C₂⁴×C₁₄₉
prime radical	C₂⁵×C₁₄₉	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₄₉ ◁ G

674 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	#34042913, #34042928, #34042930, …
maximal subgroup of	C₂²⋊#95×C₁₄₉, #1437×C₁₄₉, #1438×C₁₄₉, …
maximal normal subgroup of	C₂²⋊#95×C₁₄₉, #1437×C₁₄₉, #1438×C₁₄₉, …
maximal quotient of	C₂²×#95×C₁₄₉, C₂×C₄×C₂²⋊C₄×C₁₄₉, C₂×#379×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 193);