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C₂²×C₃×C₇×C₉×C₁₉ #72192522

order	14364
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 69984
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂²×C₃×C₇×C₉×C₁₉
multiplicative	(ℤ/15523)ˣ, (ℤ/17689)ˣ, (ℤ/31046)ˣ, (ℤ/35378)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃²×C₇×C₁₉
socle, prime radical	C₂²×C₃²×C₇×C₁₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₇×C₉×C₁₉, C₂³×C₃×C₇×C₉×C₁₉
maximal normal subgroup of	C₂×C₃×C₄×C₇×C₉×C₁₉, C₂³×C₃×C₇×C₉×C₁₉
maximal quotient of	C₂×C₃×C₄×C₇×C₉×C₁₉, C₂³×C₃×C₇×C₉×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.