Finite Group Databasebeta

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C₃×C₈×C₁₃×C₃₁ #72188381

order	9672
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃²×C₄×C₅ (order 2880) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃²×C₄×C₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₆₇₂
abelian	C₃×C₈×C₁₃×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₁₃×C₃₁
socle, prime radical	C₂×C₃×C₁₃×C₃₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9672 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₆₇₂, D₁₉₃₄₄
maximal subgroup of	C₂×C₃×C₈×C₁₃×C₃₁, C₃×C₁₃×C₁₆×C₃₁, C₈×C₉×C₁₃×C₃₁, …
maximal normal subgroup of	C₂×C₃×C₈×C₁₃×C₃₁, C₃×C₁₃×C₁₆×C₃₁, C₈×C₉×C₁₃×C₃₁, …
maximal quotient of	C₂×C₃×C₈×C₁₃×C₃₁, C₃×C₁₃×C₁₆×C₃₁, C₈×C₉×C₁₃×C₃₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.