Finite Group Databasebeta

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C₁₃×C₁₇×C₃₂ #72186140

order	7072
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄×C₈×C₁₆ (order 3072) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄×C₈×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₀₇₂
abelian	C₁₃×C₁₇×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₁₃×C₁₇
socle, prime radical	C₂×C₁₃×C₁₇	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7072 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₄₁₄₄, Dic₇₀₇₂
maximal subgroup of	C₁₃×C₁₇×C₆₄, C₂×C₁₃×C₁₇×C₃₂, C₃×C₁₃×C₁₇×C₃₂, …
maximal normal subgroup of	C₁₃×C₁₇×C₆₄, C₂×C₁₃×C₁₇×C₃₂, C₃×C₁₃×C₁₇×C₃₂, …
maximal quotient of	C₁₃×C₁₇×C₆₄, C₂×C₁₃×C₁₇×C₃₂, C₃×C₁₃×C₁₇×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.