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C₉×C₁₉×C₆₄ #72189478

order	10944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₉×C₁₆ (order 3456) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₉×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₉₄₄
abelian	C₉×C₁₉×C₆₄

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₃₂	C₂×C₃×C₁₉
socle, prime radical	C₂×C₃×C₁₉	C₃×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

42 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10944 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₉₄₄, D₂₁₈₈₈
maximal subgroup of	C₉×C₁₉×C₁₂₈, C₂×C₉×C₁₉×C₆₄, D₁₀₉₄₄, …
maximal normal subgroup of	C₉×C₁₉×C₁₂₈, C₂×C₉×C₁₉×C₆₄, D₁₀₉₄₄, …
maximal quotient of	C₉×C₁₉×C₁₂₈, C₂×C₉×C₁₉×C₆₄

GAP

Past the SmallGroups library coverage — no SmallGroups id.