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C₉×C₁₆×C₈₃ #72190355

order	11952
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄×C₄₁ (order 3936) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄×C₄₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₉₅₂
abelian	C₉×C₁₆×C₈₃
multiplicative	(ℤ/11953)ˣ, (ℤ/23906)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂×C₃×C₈₃
socle, prime radical	C₂×C₃×C₈₃	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11952 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₁₉₅₂, D₂₃₉₀₄
maximal subgroup of	C₉×C₃₂×C₈₃, C₂×C₉×C₁₆×C₈₃, D₁₁₉₅₂, …
maximal normal subgroup of	C₉×C₃₂×C₈₃, C₂×C₉×C₁₆×C₈₃, D₁₁₉₅₂, …
maximal quotient of	C₉×C₃₂×C₈₃, C₂×C₉×C₁₆×C₈₃
automorphism group of	C₁₁₉₅₃
outer automorphism group of	C₁₁₉₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.