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C₂³×C₃×C₇×C₉×C₁₁ #72194635

order	16632
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1088640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃

Aliases

abelian	C₂³×C₃×C₇×C₉×C₁₁
multiplicative	(ℤ/18791)ˣ, (ℤ/20447)ˣ, (ℤ/21413)ˣ, (ℤ/25527)ˣ, (ℤ/25671)ˣ, (ℤ/26289)ˣ, (ℤ/26391)ˣ, (ℤ/26703)ˣ, (ℤ/29253)ˣ, (ℤ/30429)ˣ, (ℤ/34036)ˣ, (ℤ/34228)ˣ, (ℤ/35188)ˣ, (ℤ/37582)ˣ, (ℤ/39004)ˣ, (ℤ/40894)ˣ, (ℤ/42826)ˣ, (ℤ/50004)ˣ, (ℤ/51054)ˣ, (ℤ/51342)ˣ, (ℤ/52578)ˣ, (ℤ/52782)ˣ, (ℤ/53406)ˣ, (ℤ/58506)ˣ, (ℤ/60858)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂³×C₃²×C₇×C₁₁
socle, prime radical	C₂³×C₃²×C₇×C₁₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

640 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16632 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₁₉×C₂₃×C₄₃, C₂₃×C₂₇×C₄₃, C₂₃×C₂₇×C₄₉
outer automorphism group of	C₁₉×C₂₃×C₄₃, C₂₃×C₂₇×C₄₃, C₂₃×C₂₇×C₄₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.