Finite Group Databasebeta

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C₃×C₉×C₁₆×C₂₇ #72190093

order	11664
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 11337408
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃²×C₉

Aliases

C₃×C₉×C₁₆×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈×C₉	C₂×C₃³
socle, prime radical	C₂×C₃³	C₃×C₈×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

1010 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11664 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₉×C₂₇×C₃₂, C₂×C₃×C₉×C₁₆×C₂₇
maximal normal subgroup of	C₃×C₉×C₂₇×C₃₂, C₂×C₃×C₉×C₁₆×C₂₇
maximal quotient of	C₃×C₉×C₂₇×C₃₂, C₂×C₃×C₉×C₁₆×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.