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C₃²×C₈×C₉×C₁₃ #72187293

order	8424
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1119744
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₃²×C₈×C₉×C₁₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂×C₃³×C₁₃
socle, prime radical	C₂×C₃³×C₁₃	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

400 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₉×C₁₃×C₁₆, C₂×C₃²×C₈×C₉×C₁₃, C₃²×C₈×C₁₃×C₂₇, …
maximal normal subgroup of	C₃²×C₉×C₁₃×C₁₆, C₂×C₃²×C₈×C₉×C₁₃, C₃²×C₈×C₁₃×C₂₇, …
maximal quotient of	C₃²×C₉×C₁₃×C₁₆, C₂×C₃²×C₈×C₉×C₁₃, C₃²×C₈×C₁₃×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.