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C₃³×C₄²×C₁₃ #72184876

order	5616
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 12939264
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₄

Aliases

C₃³×C₄²×C₁₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃³×C₁₃
socle, prime radical	C₂²×C₃³×C₁₃	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

840 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃³×C₄×C₈×C₁₃, C₂×C₃³×C₄²×C₁₃, C₃²×C₄²×C₉×C₁₃, …
maximal normal subgroup of	C₃³×C₄×C₈×C₁₃, C₂×C₃³×C₄²×C₁₃, C₃²×C₄²×C₉×C₁₃, …
maximal quotient of	C₃³×C₄×C₈×C₁₃, C₂×C₃³×C₄²×C₁₃, C₃²×C₄²×C₉×C₁₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.