Finite Group Databasebeta

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C₂×C₁₃×C₆₂₅ #72194211

order	16250
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₃×C₄²×C₁₂₅ (order 6000) · Inn(G) = C₁ · Out(G) = C₃×C₄²×C₁₂₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₂₅₀
abelian	C₂×C₁₃×C₆₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₂₅	C₂×C₅×C₁₃
socle, prime radical	C₂×C₅×C₁₃	C₁₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16250 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₆₂₅₀, D₃₂₅₀₀
Fitting subgroup of	Dic₈₁₂₅, C₂×D₈₁₂₅
maximal subgroup of	C₄×C₁₃×C₆₂₅, C₂²×C₁₃×C₆₂₅, Dic₈₁₂₅, …
maximal normal subgroup of	C₄×C₁₃×C₆₂₅, C₂²×C₁₃×C₆₂₅, Dic₈₁₂₅, …
maximal quotient of	C₄×C₁₃×C₆₂₅, C₂²×C₁₃×C₆₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.