Finite Group Databasebeta

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C₇×C₈×C₉×C₁₉ #72188285

order	9576
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁵×C₃²×C₉ (order 2592) · Inn(G) = C₁ · Out(G) = C₂⁵×C₃²×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₅₇₆
abelian	C₇×C₈×C₉×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂×C₃×C₇×C₁₉
socle, prime radical	C₂×C₃×C₇×C₁₉	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9576 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₅₇₆, D₁₉₁₅₂
maximal subgroup of	C₇×C₉×C₁₆×C₁₉, C₂×C₇×C₈×C₉×C₁₉, C₇×C₈×C₁₉×C₂₇, …
maximal normal subgroup of	C₇×C₉×C₁₆×C₁₉, C₂×C₇×C₈×C₉×C₁₉, C₇×C₈×C₁₉×C₂₇, …
maximal quotient of	C₇×C₉×C₁₆×C₁₉, C₂×C₇×C₈×C₉×C₁₉, C₇×C₈×C₁₉×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.