Finite Group Databasebeta

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C₂×C₅×C₂₇×C₅₃ #72192437

order	14310
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄²×C₉×C₁₃ (order 3744) · Inn(G) = C₁ · Out(G) = C₂×C₄²×C₉×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₃₁₀
abelian	C₂×C₅×C₂₇×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₅×C₅₃
socle, prime radical	C₂×C₃×C₅×C₅₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14310 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₄₃₁₀, D₂₈₆₂₀
Fitting subgroup of	C₂×D₇₁₅₅, Dic₇₁₅₅
maximal subgroup of	C₄×C₅×C₂₇×C₅₃, C₂²×C₅×C₂₇×C₅₃, C₂×D₇₁₅₅, …
maximal normal subgroup of	C₄×C₅×C₂₇×C₅₃, C₂²×C₅×C₂₇×C₅₃, C₂×D₇₁₅₅, …
maximal quotient of	C₄×C₅×C₂₇×C₅₃, C₂²×C₅×C₂₇×C₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.