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C₄×M₁₆×C₁₄₉ #23749161

order	9536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₄₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

C₄×M₁₆×C₁₄₉

Subgroups

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

142 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	#34042529, #34042542, #34042556, …
maximal subgroup of	#1278×C₁₄₉, #1283×C₁₄₉, #1288×C₁₄₉, …
maximal normal subgroup of	#1278×C₁₄₉, #1283×C₁₄₉, #1288×C₁₄₉, …
maximal quotient of	C₈×M₁₆×C₁₄₉, #1451×C₁₄₉, #1453×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 85);