Finite Group Databasebeta

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C₃×C₄×C₁₃×C₁₂₅ #72197175

order	19500
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄²×C₂₅ (order 4800) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄²×C₂₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₉₅₀₀
abelian	C₃×C₄×C₁₃×C₁₂₅
multiplicative	(ℤ/19501)ˣ, (ℤ/39002)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₂₅	C₂×C₃×C₅×C₁₃
socle, prime radical	C₂×C₃×C₅×C₁₃	C₂×C₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

19500 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₉₇₅₀, D₁₉₅₀₀
maximal subgroup of	Dic₉₇₅₀, D₁₉₅₀₀
maximal normal subgroup of	Dic₉₇₅₀, D₁₉₅₀₀
automorphism group of	C₁₉₅₀₁
outer automorphism group of	C₁₉₅₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.