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C₂×C₈×C₁₇×C₅₃ #72192588

order	14416
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 13312
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₈×C₁₇×C₅₃
multiplicative	(ℤ/14659)ˣ, (ℤ/29318)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₁₇×C₅₃
socle, prime radical	C₂²×C₁₇×C₅₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14416 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₆×C₁₇×C₅₃, C₄×C₈×C₁₇×C₅₃, C₂²×C₈×C₁₇×C₅₃
maximal normal subgroup of	C₂×C₁₆×C₁₇×C₅₃, C₄×C₈×C₁₇×C₅₃, C₂²×C₈×C₁₇×C₅₃
maximal quotient of	C₂×C₁₆×C₁₇×C₅₃, C₄×C₈×C₁₇×C₅₃, C₂²×C₈×C₁₇×C₅₃
automorphism group of	C₁₀₇×C₁₃₇
outer automorphism group of	C₁₀₇×C₁₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.