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C₃×C₁₃×C₁₂₈ #72184352

order	4992
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄×C₃₂ (order 1536) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄×C₃₂
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₄₉₉₂
abelian	C₃×C₁₃×C₁₂₈
multiplicative	(ℤ/4993)ˣ, (ℤ/9986)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₆₄	C₂×C₃×C₁₃
socle, prime radical	C₂×C₃×C₁₃	C₆₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4992 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₃×C₂₅₆, C₂×C₃×C₁₃×C₁₂₈, C₉×C₁₃×C₁₂₈, …
maximal normal subgroup of	C₃×C₁₃×C₂₅₆, C₂×C₃×C₁₃×C₁₂₈, C₉×C₁₃×C₁₂₈, …
maximal quotient of	C₃×C₁₃×C₂₅₆, C₂×C₃×C₁₃×C₁₂₈, C₉×C₁₃×C₁₂₈, …
automorphism group of	C₄₉₉₃, C₂×C₄₉₉₃
outer automorphism group of	C₄₉₉₃, C₂×C₄₉₉₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.