Finite Group Databasebeta

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C₈×C₂₇×C₄₉ #72189159

order	10584
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃×C₇×C₉ (order 3024) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃×C₇×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₅₈₄
abelian	C₈×C₂₇×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₇×C₉	C₂×C₃×C₇
socle, prime radical	C₂×C₃×C₇	C₄×C₇×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10584 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₅₈₄, D₂₁₁₆₈
maximal subgroup of	C₁₆×C₂₇×C₄₉, C₂×C₈×C₂₇×C₄₉, C₈×C₄₉×C₈₁, …
maximal normal subgroup of	C₁₆×C₂₇×C₄₉, C₂×C₈×C₂₇×C₄₉, C₈×C₄₉×C₈₁, …
maximal quotient of	C₁₆×C₂₇×C₄₉, C₂×C₈×C₂₇×C₄₉, C₈×C₄₉×C₈₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.