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#519×C₂₆₃ #30681589

order	16832
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₆₃ · Schur multiplier (H₂) = C₂⁵

Aliases

#519×C₂₆₃

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₆₃	C₂⁴
commutator	C₂	C₂³×C₄×C₂₆₃
Frattini, cosocle	C₂²	C₂⁴×C₂₆₃
prime radical	C₂³×C₂₆₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₆₃ ◁ G

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8416

Conjugacy classes & character table

8942 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#46782861, #46782962, #46783140, …
maximal subgroup of	#1830×C₂₆₃, #1857×C₂₆₃, #1886×C₂₆₃, …
maximal normal subgroup of	#1830×C₂₆₃, #1857×C₂₆₃, #1886×C₂₆₃, …
maximal quotient of	#2274×C₂₆₃, #2276×C₂₆₃, #2310×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 200);