Finite Group Databasebeta

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C₃×C₈×C₃₁₁ #72186443

order	7464
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₅×C₃₁ (order 2480) · Inn(G) = C₁ · Out(G) = C₂⁴×C₅×C₃₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₄₆₄
abelian	C₃×C₈×C₃₁₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₃₁₁
socle, prime radical	C₂×C₃×C₃₁₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7464 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₄₉₂₈, Dic₇₄₆₄
maximal subgroup of	C₃×C₁₆×C₃₁₁, C₂×C₃×C₈×C₃₁₁, C₈×C₉×C₃₁₁, …
maximal normal subgroup of	C₃×C₁₆×C₃₁₁, C₂×C₃×C₈×C₃₁₁, C₈×C₉×C₃₁₁, …
maximal quotient of	C₃×C₁₆×C₃₁₁, C₂×C₃×C₈×C₃₁₁, C₈×C₉×C₃₁₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.