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C₃³×C₂₆₉ #20300142

order	7263
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3010176
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₃³×C₂₆₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7263 conjugacy classes. The character table is too large to display.

Relationships

socle of	C₃²×C₉×C₂₆₉
maximal subgroup of	C₃²⋊C₉×C₂₆₉, AΣL(1,𝔽₂₇)×C₂₆₉, C₃²×C₉×C₂₆₉, …
maximal normal subgroup of	C₃²⋊C₉×C₂₆₉, AΣL(1,𝔽₂₇)×C₂₆₉, C₃²×C₉×C₂₆₉, …
maximal quotient of	C₃²×C₉×C₂₆₉, C₃×H(3,𝔽₃)×C₂₆₉, C₃×3₋¹⁺²×C₂₆₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7263, 5);