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C₃₂×C₃₇₃ #26045647

order	11936
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5952
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₉₃₆
abelian	C₃₂×C₃₇₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₃₇₃
socle, prime radical	C₂×C₃₇₃	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11936 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37559141, C₃₂×D₃₇₃, #37559255, …
maximal subgroup of	C₆₄×C₃₇₃, C₂×C₃₂×C₃₇₃, M₆₄×C₃₇₃, …
maximal normal subgroup of	C₆₄×C₃₇₃, C₂×C₃₂×C₃₇₃, M₆₄×C₃₇₃, …
maximal quotient of	C₆₄×C₃₇₃, C₂×C₃₂×C₃₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 1);