Finite Group Databasebeta

← Prev (#22554348) Next (#22554350) →

C₄×D₄×C₂₆₃ #22554349

order	8416
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₆₃ · Schur multiplier (H₂) = C₂³

Aliases

C₄×D₄×C₂₆₃

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₆₃	C₂²
commutator	C₂	C₂²×C₄×C₂₆₃
Frattini, cosocle	C₂²	C₂³×C₂₆₃
socle	C₂²×C₂₆₃	C₂³
prime radical	C₂×D₄×C₂₆₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₆₃ ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5260 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	D₄⋊(C₂₆₃⋊C₈), D₄×C₂₆₃⋊C₈, #30682010, …
maximal subgroup of	D₄⋊C₈×C₂₆₃, C₈×D₄×C₂₆₃, #435×C₂₆₃, …
maximal normal subgroup of	D₄⋊C₈×C₂₆₃, C₈×D₄×C₂₆₃, #435×C₂₆₃, …
maximal quotient of	C₄×C₂²⋊C₄×C₂₆₃, C₄×C₄⋊C₄×C₂₆₃, #385×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8416, 25);