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C₅×C₃₂×C₅₃ #72187353

order	8480
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄²×C₈×C₁₃ (order 3328) · Inn(G) = C₁ · Out(G) = C₂×C₄²×C₈×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₄₈₀
abelian	C₅×C₃₂×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₅×C₅₃
socle, prime radical	C₂×C₅×C₅₃	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8480 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₈₄₈₀, D₁₆₉₆₀
maximal subgroup of	C₅×C₅₃×C₆₄, C₂×C₅×C₃₂×C₅₃, C₃×C₅×C₃₂×C₅₃, …
maximal normal subgroup of	C₅×C₅₃×C₆₄, C₂×C₅×C₃₂×C₅₃, C₃×C₅×C₃₂×C₅₃, …
maximal quotient of	C₅×C₅₃×C₆₄, C₂×C₅×C₃₂×C₅₃, C₃×C₅×C₃₂×C₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.