Finite Group Databasebeta

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C₂×C₆₁×C₁₂₅ #72193264

order	15250
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₃×C₄²×C₅×C₂₅ (order 6000) · Inn(G) = C₁ · Out(G) = C₃×C₄²×C₅×C₂₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₅₂₅₀
abelian	C₂×C₆₁×C₁₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₅	C₂×C₅×C₆₁
socle, prime radical	C₂×C₅×C₆₁	C₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15250 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₅₂₅₀, D₃₀₅₀₀
Fitting subgroup of	C₂×D₇₆₂₅, Dic₇₆₂₅
maximal subgroup of	C₄×C₆₁×C₁₂₅, C₂²×C₆₁×C₁₂₅, C₂×D₇₆₂₅, …
maximal normal subgroup of	C₄×C₆₁×C₁₂₅, C₂²×C₆₁×C₁₂₅, C₂×D₇₆₂₅, …
maximal quotient of	C₄×C₆₁×C₁₂₅, C₂²×C₆₁×C₁₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.