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C₂³×C₃³×C₁₃ #72182638

order	2808
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 22643712
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃³

Aliases

abelian	C₂³×C₃³×C₁₃
multiplicative	(ℤ/4977)ˣ, (ℤ/9954)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

896 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2808 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃³×C₄×C₁₃, C₂⁴×C₃³×C₁₃, C₂³×C₃⁴×C₁₃, …
maximal normal subgroup of	C₂²×C₃³×C₄×C₁₃, C₂⁴×C₃³×C₁₃, C₂³×C₃⁴×C₁₃, …
maximal quotient of	C₂²×C₃³×C₄×C₁₃, C₂⁴×C₃³×C₁₃, C₂³×C₃⁴×C₁₃, …
automorphism group of	C₇×C₉×C₇₉, C₂×C₇×C₉×C₇₉
outer automorphism group of	C₇×C₉×C₇₉, C₂×C₇×C₉×C₇₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.