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C₂×C₂₇×C₂₄₁ #72191306

order	13014
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₅×C₉×C₁₆ (order 4320) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₅×C₉×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₀₁₄
abelian	C₂×C₂₇×C₂₄₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₂₄₁
socle, prime radical	C₂×C₃×C₂₄₁	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13014 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₀₁₄, D₂₆₀₂₈
Fitting subgroup of	C₂×D₆₅₀₇, Dic₆₅₀₇
maximal subgroup of	C₄×C₂₇×C₂₄₁, C₂²×C₂₇×C₂₄₁, C₂×D₆₅₀₇, …
maximal normal subgroup of	C₄×C₂₇×C₂₄₁, C₂²×C₂₇×C₂₄₁, C₂×D₆₅₀₇, …
maximal quotient of	C₄×C₂₇×C₂₄₁, C₂²×C₂₇×C₂₄₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.