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C₄⋊C₈×C₃₇₃ #26045658

order	11936
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₃₇₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₄⋊C₈×C₃₇₃
unambiguous semidirect product	C₄⋊(C₈×C₃₇₃)

Subgroups

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

38 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	#37559149, #37559152, #37559165, …
maximal subgroup of	D₄⋊C₈×C₃₇₃, Q₈⋊C₈×C₃₇₃, #331×C₃₇₃, …
maximal normal subgroup of	D₄⋊C₈×C₃₇₃, Q₈⋊C₈×C₃₇₃, #331×C₃₇₃, …
maximal quotient of	#334×C₃₇₃, #335×C₃₇₃, #336×C₃₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 12);