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C₂×C₅×C₁₃×C₂₇ #72183168

order	3510
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄²×C₉ (order 864) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄²×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₅₁₀
abelian	C₂×C₅×C₁₃×C₂₇
multiplicative	(ℤ/3511)ˣ, (ℤ/7022)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₅×C₁₃
socle, prime radical	C₂×C₃×C₅×C₁₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3510 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₅×C₁₃×C₂₇, C₂²×C₅×C₁₃×C₂₇, C₂×C₅×C₁₃×C₈₁, …
maximal normal subgroup of	C₄×C₅×C₁₃×C₂₇, C₂²×C₅×C₁₃×C₂₇, C₂×C₅×C₁₃×C₈₁, …
maximal quotient of	C₄×C₅×C₁₃×C₂₇, C₂²×C₅×C₁₃×C₂₇, C₂×C₅×C₁₃×C₈₁, …
automorphism group of	C₃₅₁₁, C₂×C₃₅₁₁
outer automorphism group of	C₃₅₁₁, C₂×C₃₅₁₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.