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C₂×C₃×C₉×C₁₃×C₁₆ #72189710

order	11232
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 41472
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂×C₃×C₉×C₁₃×C₁₆
multiplicative	(ℤ/13111)ˣ, (ℤ/16857)ˣ, (ℤ/26222)ˣ, (ℤ/33714)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂²×C₃²×C₁₃
socle, prime radical	C₂²×C₃²×C₁₃	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₉×C₁₃×C₃₂, C₃×C₄×C₉×C₁₃×C₁₆, C₂²×C₃×C₉×C₁₃×C₁₆
maximal normal subgroup of	C₂×C₃×C₉×C₁₃×C₃₂, C₃×C₄×C₉×C₁₃×C₁₆, C₂²×C₃×C₉×C₁₃×C₁₆
maximal quotient of	C₂×C₃×C₉×C₁₃×C₃₂, C₃×C₄×C₉×C₁₃×C₁₆, C₂²×C₃×C₉×C₁₃×C₁₆
automorphism group of	C₇×C₁₈₇₃
outer automorphism group of	C₇×C₁₈₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.