Finite Group Databasebeta

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C₃×C₉×C₁₆×C₃₂ #72192004

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3538944
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₁₆

Aliases

C₃×C₉×C₁₆×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈×C₁₆	C₂²×C₃²
socle, prime radical	C₂²×C₃²	C₃×C₈×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

1140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₉×C₁₆×C₆₄, C₃×C₉×C₃₂², C₂×C₃×C₉×C₁₆×C₃₂
maximal normal subgroup of	C₃×C₉×C₁₆×C₆₄, C₃×C₉×C₃₂², C₂×C₃×C₉×C₁₆×C₃₂
maximal quotient of	C₃×C₉×C₁₆×C₆₄, C₃×C₉×C₃₂², C₂×C₃×C₉×C₁₆×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.