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C₃×C₈×C₁₆×C₁₇ #72185657

order	6528
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 65536
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₈

Aliases

abelian	C₃×C₈×C₁₆×C₁₇
multiplicative	(ℤ/6953)ˣ, (ℤ/13906)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂²×C₃×C₁₇
socle, prime radical	C₂²×C₃×C₁₇	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

208 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₈×C₁₇×C₃₂, C₃×C₁₆²×C₁₇, C₂×C₃×C₈×C₁₆×C₁₇, …
maximal normal subgroup of	C₃×C₈×C₁₇×C₃₂, C₃×C₁₆²×C₁₇, C₂×C₃×C₈×C₁₆×C₁₇, …
maximal quotient of	C₃×C₈×C₁₇×C₃₂, C₃×C₁₆²×C₁₇, C₂×C₃×C₈×C₁₆×C₁₇, …
automorphism group of	C₁₇×C₄₀₉
outer automorphism group of	C₁₇×C₄₀₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.