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C₃×C₅²×C₉×C₁₆ #72189335

order	10800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 414720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₅

Aliases

C₃×C₅²×C₉×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂×C₃²×C₅²
socle, prime radical	C₂×C₃²×C₅²	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

400 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅²×C₉×C₃₂, C₂×C₃×C₅²×C₉×C₁₆, C₃×C₅²×C₁₆×C₂₇, …
maximal normal subgroup of	C₃×C₅²×C₉×C₃₂, C₂×C₃×C₅²×C₉×C₁₆, C₃×C₅²×C₁₆×C₂₇, …
maximal quotient of	C₃×C₅²×C₉×C₃₂, C₂×C₃×C₅²×C₉×C₁₆, C₃×C₅²×C₁₆×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.