Finite Group Databasebeta

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#131×C₃₇₃ #26045684

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

Aliases

#131×C₃₇₃

Subgroups

	subgroup	G/H
center	C₈×C₃₇₃	C₂²
commutator	C₂	C₂²×C₄×C₃₇₃
Frattini, cosocle	C₄	C₂³×C₃₇₃
socle	C₂×C₃₇₃	C₂²×C₄
prime radical	#41×C₃₇₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₇₃ ◁ G

62 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	#37559206, #37559537, #37559542, …
maximal subgroup of	#350×C₃₇₃, #443×C₃₇₃, #444×C₃₇₃, …
maximal normal subgroup of	#350×C₃₇₃, #443×C₃₇₃, #444×C₃₇₃, …
maximal quotient of	#405×C₃₇₃, #408×C₃₇₃, #424×C₃₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 38);