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C₃×C₇×C₉×C₁₉ #72183253

order	3591
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 11664
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃×C₇×C₉×C₁₉

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3591 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₇×C₉×C₁₉, C₇×C₉²×C₁₉, C₃×C₇×C₁₉×C₂₇, …
maximal normal subgroup of	C₂×C₃×C₇×C₉×C₁₉, C₇×C₉²×C₁₉, C₃×C₇×C₁₉×C₂₇, …
maximal quotient of	C₂×C₃×C₇×C₉×C₁₉, C₇×C₉²×C₁₉, C₃×C₇×C₁₉×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.