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C₂₇×C₂₈₉ #72186744

order	7803
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₉×C₁₆×C₁₇ (order 4896) · Inn(G) = C₁ · Out(G) = C₂×C₉×C₁₆×C₁₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₈₀₃
abelian	C₂₇×C₂₈₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉×C₁₇	C₃×C₁₇
socle, prime radical	C₃×C₁₇	C₉×C₁₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7803 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₇₈₀₃, C₂×D₇₈₀₃
maximal subgroup of	C₂×C₂₇×C₂₈₉, C₈₁×C₂₈₉, C₃×C₂₇×C₂₈₉, …
maximal normal subgroup of	C₂×C₂₇×C₂₈₉, C₈₁×C₂₈₉, C₃×C₂₇×C₂₈₉, …
maximal quotient of	C₂×C₂₇×C₂₈₉, C₈₁×C₂₈₉, C₃×C₂₇×C₂₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.