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C₅×C₈×C₂₄₃ #72188404

order	9720
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₄×C₈₁ (order 2592) · Inn(G) = C₁ · Out(G) = C₂³×C₄×C₈₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₇₂₀
abelian	C₅×C₈×C₂₄₃
multiplicative	(ℤ/9721)ˣ, (ℤ/19442)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈₁	C₂×C₃×C₅
socle, prime radical	C₂×C₃×C₅	C₄×C₈₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9720 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₇₂₀, D₁₉₄₄₀
maximal subgroup of	C₅×C₁₆×C₂₄₃, C₂×C₅×C₈×C₂₄₃, C₅×C₈×C₇₂₉, …
maximal normal subgroup of	C₅×C₁₆×C₂₄₃, C₂×C₅×C₈×C₂₄₃, C₅×C₈×C₇₂₉, …
maximal quotient of	C₅×C₁₆×C₂₄₃, C₂×C₅×C₈×C₂₄₃, C₅×C₈×C₇₂₉, …
automorphism group of	C₉₇₂₁
outer automorphism group of	C₉₇₂₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.