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C₂×M₁₆×C₃₇₃ #26045683

order	11936
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇₃ · Schur multiplier (H₂) = C₂²

Aliases

C₂×M₁₆×C₃₇₃

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇₃	C₂²
commutator	C₂	C₂²×C₄×C₃₇₃
Frattini, cosocle	C₄	C₂³×C₃₇₃
socle	C₂²×C₃₇₃	C₂×C₄
prime radical	C₂³×C₃₇₃	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇₃ ◁ G

68 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7460 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37559179, #37559180, #37559183, …
maximal subgroup of	H(3,ℤ/4)×C₃₇₃, #338×C₃₇₃, #339×C₃₇₃, …
maximal normal subgroup of	H(3,ℤ/4)×C₃₇₃, #338×C₃₇₃, #339×C₃₇₃, …
maximal quotient of	C₂×#97×C₃₇₃, C₄×M₁₆×C₃₇₃, C₂×C₂²⋊C₈×C₃₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 37);