Finite Group Databasebeta

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C₃×C₁₆×C₃₂ #72181973

order	1536
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 65536
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₆

Aliases

abelian	C₃×C₁₆×C₃₂
multiplicative	(ℤ/1649)ˣ, (ℤ/3298)ˣ

Subgroups

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

228 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1536 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₆×C₆₄, C₃×C₃₂², C₂×C₃×C₁₆×C₃₂, …
maximal normal subgroup of	C₃×C₁₆×C₆₄, C₃×C₃₂², C₂×C₃×C₁₆×C₃₂, …
maximal quotient of	C₃×C₁₆×C₆₄, C₃×C₃₂², C₂×C₃×C₁₆×C₃₂, …
automorphism group of	C₁₇×C₉₇, C₂×C₁₇×C₉₇
outer automorphism group of	C₁₇×C₉₇, C₂×C₁₇×C₉₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.