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#104×C₃₇₃ #26045657

order	11936
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₇₃ · Schur multiplier (H₂) = C₂

Aliases

#104×C₃₇₃

Subgroups

	subgroup	G/H
center	C₄×C₃₇₃	D₄
commutator	C₄	C₂×C₄×C₃₇₃
Frattini, cosocle	C₂×C₄	C₂²×C₃₇₃
socle	C₂×C₃₇₃	C₂²⋊C₄
prime radical	#41×C₃₇₃	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇₃ ◁ C₂×C₄×C₃₇₃ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5222 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#104×D₃₇₃, #37559437, #37559536, …
maximal subgroup of	C₂×#104×C₃₇₃, #421×C₃₇₃, #443×C₃₇₃, …
maximal normal subgroup of	C₂×#104×C₃₇₃, #421×C₃₇₃, #443×C₃₇₃, …
maximal quotient of	D₄⋊C₈×C₃₇₃, Q₈⋊C₈×C₃₇₃, #327×C₃₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 11);