Finite Group Databasebeta

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C₃×C₉×C₁₃×C₃₂ #72189707

order	11232
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 20736
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃×C₉×C₁₃×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₁₆	C₂×C₃²×C₁₃
socle, prime radical	C₂×C₃²×C₁₃	C₃×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₉×C₁₃×C₆₄, C₂×C₃×C₉×C₁₃×C₃₂
maximal normal subgroup of	C₃×C₉×C₁₃×C₆₄, C₂×C₃×C₉×C₁₃×C₃₂
maximal quotient of	C₃×C₉×C₁₃×C₆₄, C₂×C₃×C₉×C₁₃×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.