Finite Group Databasebeta

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C₁₃×C₂₇×C₃₂ #72189705

order	11232
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄×C₈×C₉ (order 3456) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄×C₈×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₂₃₂
abelian	C₁₃×C₂₇×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉×C₁₆	C₂×C₃×C₁₃
socle, prime radical	C₂×C₃×C₁₃	C₉×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

derived subgroup of	Dic₁₁₂₃₂, D₂₂₄₆₄
maximal subgroup of	C₁₃×C₂₇×C₆₄, C₂×C₁₃×C₂₇×C₃₂, D₁₁₂₃₂, …
maximal normal subgroup of	C₁₃×C₂₇×C₆₄, C₂×C₁₃×C₂₇×C₃₂, D₁₁₂₃₂, …
maximal quotient of	C₁₃×C₂₇×C₆₄, C₂×C₁₃×C₂₇×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.