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C₈×C₉×C₄₉ #72183182

order	3528
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃²×C₇ (order 1008) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃²×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₅₂₈
abelian	C₈×C₉×C₄₉
multiplicative	(ℤ/3529)ˣ, (ℤ/7058)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄×C₇	C₂×C₃×C₇
socle, prime radical	C₂×C₃×C₇	C₃×C₄×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₁₆×C₄₉, C₂×C₈×C₉×C₄₉, C₈×C₂₇×C₄₉, …
maximal normal subgroup of	C₉×C₁₆×C₄₉, C₂×C₈×C₉×C₄₉, C₈×C₂₇×C₄₉, …
maximal quotient of	C₉×C₁₆×C₄₉, C₂×C₈×C₉×C₄₉, C₈×C₂₇×C₄₉, …
automorphism group of	C₃₅₂₉, C₂×C₃₅₂₉
outer automorphism group of	C₃₅₂₉, C₂×C₃₅₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.