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C₂²⋊C₁₆×C₁₄₉ #23749105

order	9536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₄₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂²⋊C₁₆×C₁₄₉
unambiguous semidirect product	C₂²⋊(C₁₆×C₁₄₉)

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₄₉	C₂²
commutator	C₂	C₂×C₁₆×C₁₄₉
Frattini, cosocle	C₂×C₈	C₂²×C₁₄₉
socle	C₂²×C₁₄₉	C₂×C₈
prime radical	C₂³×C₁₄₉	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×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	#34042614, #34042616, #34042630, …
maximal subgroup of	#1314×C₁₄₉, #1315×C₁₄₉, #1322×C₁₄₉, …
maximal normal subgroup of	#1314×C₁₄₉, #1315×C₁₄₉, #1322×C₁₄₉, …
maximal quotient of	#1314×C₁₄₉, #1322×C₁₄₉, D₄⋊C₁₆×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 29);