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#100×C₂₆₃ #22554331

order	8416
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₆₃ · Schur multiplier (H₂) = C₂

Aliases

#100×C₂₆₃

Subgroups

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

46 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2893 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30681726, #30681729, #100×D₂₆₃, …
maximal subgroup of	AΣL(1,𝔽₁₆)×C₂₆₃, #352×C₂₆₃, C₂×#100×C₂₆₃, …
maximal normal subgroup of	AΣL(1,𝔽₁₆)×C₂₆₃, #352×C₂₆₃, C₂×#100×C₂₆₃, …
maximal quotient of	#323×C₂₆₃, #329×C₂₆₃, #331×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8416, 7);