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C₄×D₄×C₃₇₃ #26045671

order	11936
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇₃ · Schur multiplier (H₂) = C₂³

Aliases

C₄×D₄×C₃₇₃

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇₃	C₂²
commutator	C₂	C₂²×C₄×C₃₇₃
Frattini, cosocle	C₂²	C₂³×C₃₇₃
socle	C₂²×C₃₇₃	C₂³
prime radical	C₂×D₄×C₃₇₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇₃ ◁ G

94 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	D₄⋊#15688412, D₄×#15688412, #37559494, …
maximal subgroup of	D₄⋊C₈×C₃₇₃, C₈×D₄×C₃₇₃, #435×C₃₇₃, …
maximal normal subgroup of	D₄⋊C₈×C₃₇₃, C₈×D₄×C₃₇₃, #435×C₃₇₃, …
maximal quotient of	C₄×C₂²⋊C₄×C₃₇₃, C₄×C₄⋊C₄×C₃₇₃, #385×C₃₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 25);