Finite Group Databasebeta

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C₃×C₁₉×C₁₂₅ #72186172

order	7125
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₉×C₂₅ (order 3600) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₉×C₂₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₁₂₅
abelian	C₃×C₁₉×C₁₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₅	C₃×C₅×C₁₉
socle, prime radical	C₃×C₅×C₁₉	C₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7125 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	C₂×D₇₁₂₅, Dic₇₁₂₅
maximal subgroup of	C₂×C₃×C₁₉×C₁₂₅, C₉×C₁₉×C₁₂₅, C₃²×C₁₉×C₁₂₅, …
maximal normal subgroup of	C₂×C₃×C₁₉×C₁₂₅, C₉×C₁₉×C₁₂₅, C₃²×C₁₉×C₁₂₅, …
maximal quotient of	C₂×C₃×C₁₉×C₁₂₅, C₉×C₁₉×C₁₂₅, C₃²×C₁₉×C₁₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.