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C₄²×C₅×C₉×C₁₆ #72189952

order	11520
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4718592
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

abelian	C₄²×C₅×C₉×C₁₆
multiplicative	(ℤ/15385)ˣ, (ℤ/15725)ˣ, (ℤ/30770)ˣ, (ℤ/31450)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃×C₈	C₂³×C₃×C₅
socle, prime radical	C₂³×C₃×C₅	C₂²×C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

1674 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄²×C₅×C₉×C₃₂, C₄×C₅×C₈×C₉×C₁₆, C₂×C₄²×C₅×C₉×C₁₆
maximal normal subgroup of	C₄²×C₅×C₉×C₃₂, C₄×C₅×C₈×C₉×C₁₆, C₂×C₄²×C₅×C₉×C₁₆
maximal quotient of	C₄²×C₅×C₉×C₃₂, C₄×C₅×C₈×C₉×C₁₆, C₂×C₄²×C₅×C₉×C₁₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.