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C₂³×C₃×C₁₃×C₁₆ #72184359

order	4992
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2064384
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₃×C₁₃×C₁₆
multiplicative	(ℤ/10744)ˣ, (ℤ/15168)ˣ, (ℤ/16116)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂⁴×C₃×C₁₃
socle, prime radical	C₂⁴×C₃×C₁₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

880 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4992 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃×C₁₃×C₃₂, C₂⁴×C₃×C₁₃×C₁₆, C₂²×C₃×C₄×C₁₃×C₁₆, …
maximal normal subgroup of	C₂³×C₃×C₁₃×C₃₂, C₂⁴×C₃×C₁₃×C₁₆, C₂²×C₃×C₄×C₁₃×C₁₆, …
maximal quotient of	C₂³×C₃×C₁₃×C₃₂, C₂⁴×C₃×C₁₃×C₁₆, C₂²×C₃×C₄×C₁₃×C₁₆, …
automorphism group of	C₈×C₁₇×C₇₉, C₃×C₆₄×C₇₉
outer automorphism group of	C₈×C₁₇×C₇₉, C₃×C₆₄×C₇₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.