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C₂×C₉×C₁₂₅ #72182192

order	2250
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄×C₂₅ (order 600) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄×C₂₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₂₅₀
abelian	C₂×C₉×C₁₂₅
multiplicative	(ℤ/2251)ˣ, (ℤ/4502)ˣ

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2250 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₉×C₁₂₅, C₂²×C₉×C₁₂₅, C₂×C₂₇×C₁₂₅, …
maximal normal subgroup of	C₄×C₉×C₁₂₅, C₂²×C₉×C₁₂₅, C₂×C₂₇×C₁₂₅, …
maximal quotient of	C₄×C₉×C₁₂₅, C₂²×C₉×C₁₂₅, C₂×C₂₇×C₁₂₅, …
automorphism group of	C₂₂₅₁, C₂×C₂₂₅₁
outer automorphism group of	C₂₂₅₁, C₂×C₂₂₅₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.