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C₂²⋊C₄×C₆₈₃ #24926384

order	10928
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₆₈₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂²⋊C₄×C₆₈₃
unambiguous semidirect product	C₂²⋊(C₄×C₆₈₃)

Subgroups

	subgroup	G/H
center, socle	C₂²×C₆₈₃	C₂²
commutator	C₂	C₂×C₄×C₆₈₃
Frattini, cosocle	C₂²	C₂²×C₆₈₃
prime radical	C₂³×C₆₈₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₈₃ ◁ G

34 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6830 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36345930, C₂²⋊C₄×D₆₈₃, #36345972, …
maximal subgroup of	#99×C₆₈₃, C₂×C₂²⋊C₄×C₆₈₃, #117×C₆₈₃, …
maximal normal subgroup of	#99×C₆₈₃, C₂×C₂²⋊C₄×C₆₈₃, #117×C₆₈₃, …
maximal quotient of	#95×C₆₈₃, C₂²⋊C₈×C₆₈₃, #99×C₆₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10928, 3);