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C₄²×C₅×C₉×C₁₃ #72188140

order	9360
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 27648
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₅×C₉×C₁₃
multiplicative	(ℤ/9593)ˣ, (ℤ/11705)ˣ, (ℤ/19186)ˣ, (ℤ/23410)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂²×C₃×C₅×C₁₃
socle, prime radical	C₂²×C₃×C₅×C₁₃	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₅×C₈×C₉×C₁₃, C₂×C₄²×C₅×C₉×C₁₃, C₄²×C₅×C₁₃×C₂₇, …
maximal normal subgroup of	C₄×C₅×C₈×C₉×C₁₃, C₂×C₄²×C₅×C₉×C₁₃, C₄²×C₅×C₁₃×C₂₇, …
maximal quotient of	C₄×C₅×C₈×C₉×C₁₃, C₂×C₄²×C₅×C₉×C₁₃, C₄²×C₅×C₁₃×C₂₇, …
automorphism group of	C₅₃×C₁₈₁, C₅×C₂₃₄₁
outer automorphism group of	C₅₃×C₁₈₁, C₅×C₂₃₄₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.