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C₃×C₄×C₇×C₁₂₅ #72189108

order	10500
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄×C₂₅ (order 2400) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄×C₂₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₅₀₀
abelian	C₃×C₄×C₇×C₁₂₅
multiplicative	(ℤ/10501)ˣ, (ℤ/21002)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₂₅	C₂×C₃×C₅×C₇
socle, prime radical	C₂×C₃×C₅×C₇	C₂×C₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10500 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₅₀₀, D₂₁₀₀₀
maximal subgroup of	C₃×C₇×C₈×C₁₂₅, C₂×C₃×C₄×C₇×C₁₂₅, C₄×C₇×C₉×C₁₂₅, …
maximal normal subgroup of	C₃×C₇×C₈×C₁₂₅, C₂×C₃×C₄×C₇×C₁₂₅, C₄×C₇×C₉×C₁₂₅, …
maximal quotient of	C₃×C₇×C₈×C₁₂₅, C₂×C₃×C₄×C₇×C₁₂₅, C₄×C₇×C₉×C₁₂₅, …
automorphism group of	C₁₀₅₀₁
outer automorphism group of	C₁₀₅₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.