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C₂×C₂₇×C₂₃₃ #72190943

order	12582
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₈×C₉×C₂₉ (order 4176) · Inn(G) = C₁ · Out(G) = C₂×C₈×C₉×C₂₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₅₈₂
abelian	C₂×C₂₇×C₂₃₃
multiplicative	(ℤ/12583)ˣ, (ℤ/25166)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₂₃₃
socle, prime radical	C₂×C₃×C₂₃₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12582 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₂₅₈₂, D₂₅₁₆₄
maximal subgroup of	C₄×C₂₇×C₂₃₃, C₂²×C₂₇×C₂₃₃, Dic₆₂₉₁, …
maximal normal subgroup of	C₄×C₂₇×C₂₃₃, C₂²×C₂₇×C₂₃₃, Dic₆₂₉₁, …
maximal quotient of	C₄×C₂₇×C₂₃₃, C₂²×C₂₇×C₂₃₃
automorphism group of	C₁₂₅₈₃
outer automorphism group of	C₁₂₅₈₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.