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C₂₇×C₃₆₁ #72188459

order	9747
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₉²×C₁₉ (order 6156) · Inn(G) = C₁ · Out(G) = C₂²×C₉²×C₁₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₇₄₇
abelian	C₂₇×C₃₆₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉×C₁₉	C₃×C₁₉
socle, prime radical	C₃×C₁₉	C₉×C₁₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9747 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₇₄₇, C₂×D₉₇₄₇
maximal subgroup of	C₂×C₂₇×C₃₆₁, C₈₁×C₃₆₁, C₃×C₂₇×C₃₆₁, …
maximal normal subgroup of	C₂×C₂₇×C₃₆₁, C₈₁×C₃₆₁, C₃×C₂₇×C₃₆₁, …
maximal quotient of	C₂×C₂₇×C₃₆₁, C₈₁×C₃₆₁, C₃×C₂₇×C₃₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.