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C₃³×C₃₈₉ #24901877

order	10503
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4358016
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₃³×C₃₈₉

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

10503 conjugacy classes. The character table is too large to display.

Relationships

socle of	C₃²×C₉×C₃₈₉
maximal subgroup of	C₃²⋊C₉×C₃₈₉, AΣL(1,𝔽₂₇)×C₃₈₉, C₃²×C₉×C₃₈₉, …
maximal normal subgroup of	C₃²⋊C₉×C₃₈₉, AΣL(1,𝔽₂₇)×C₃₈₉, C₃²×C₉×C₃₈₉, …
maximal quotient of	C₃²×C₉×C₃₈₉, C₃×H(3,𝔽₃)×C₃₈₉, C₃×3₋¹⁺²×C₃₈₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10503, 5);