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C₂×C₁₃×C₁₆×C₁₇ #72186141

order	7072
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6144
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₁₃×C₁₆×C₁₇
multiplicative	(ℤ/7531)ˣ, (ℤ/15062)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₁₃×C₁₇
socle, prime radical	C₂²×C₁₃×C₁₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₃×C₁₇×C₃₂, C₄×C₁₃×C₁₆×C₁₇, C₂²×C₁₃×C₁₆×C₁₇, …
maximal normal subgroup of	C₂×C₁₃×C₁₇×C₃₂, C₄×C₁₃×C₁₆×C₁₇, C₂²×C₁₃×C₁₆×C₁₇, …
maximal quotient of	C₂×C₁₃×C₁₇×C₃₂, C₄×C₁₃×C₁₆×C₁₇, C₂²×C₁₃×C₁₆×C₁₇, …
automorphism group of	C₁₇×C₄₄₃
outer automorphism group of	C₁₇×C₄₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.