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C₂²×C₅×C₉×C₃₇ #20269016

order	6660
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5184
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₅×C₉×C₃₇
multiplicative	(ℤ/9993)ˣ, (ℤ/13324)ˣ, (ℤ/19986)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₃	C₂²×C₃×C₅×C₃₇
socle	C₂²×C₃×C₅×C₃₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6660 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₉×C₂₅×C₃₇, C₂²×C₅²×C₉×C₃₇, C₂×C₅×C₉×D₅×C₃₇, …
maximal normal subgroup of	C₂²×C₉×C₂₅×C₃₇, C₂²×C₅²×C₉×C₃₇, C₂×C₄×C₅×C₉×C₃₇, …
maximal quotient of	C₂²×C₉×C₂₅×C₃₇, C₂²×C₅²×C₉×C₃₇, C₂×C₅×C₉×D₅×C₃₇, …
automorphism group of	C₃×C₃₃₃₁
outer automorphism group of	C₃×C₃₃₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6660, 13);