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C₃×C₈×C₁₀₉ #72182500

order	2616
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₄×C₂₇ (order 864) · Inn(G) = C₁ · Out(G) = C₂³×C₄×C₂₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₆₁₆
abelian	C₃×C₈×C₁₀₉
multiplicative	(ℤ/2617)ˣ, (ℤ/5234)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₁₀₉
socle, prime radical	C₂×C₃×C₁₀₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₆×C₁₀₉, C₂×C₃×C₈×C₁₀₉, C₈×C₉×C₁₀₉, …
maximal normal subgroup of	C₃×C₁₆×C₁₀₉, C₂×C₃×C₈×C₁₀₉, C₈×C₉×C₁₀₉, …
maximal quotient of	C₃×C₁₆×C₁₀₉, C₂×C₃×C₈×C₁₀₉, C₈×C₉×C₁₀₉, …
automorphism group of	C₂₆₁₇, C₂×C₂₆₁₇
outer automorphism group of	C₂₆₁₇, C₂×C₂₆₁₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.