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C₂×C₃×C₈×C₁₄₉ #72186195

order	7152
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4736
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₈×C₁₄₉
multiplicative	(ℤ/8351)ˣ, (ℤ/10737)ˣ, (ℤ/16702)ˣ, (ℤ/21474)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃×C₁₄₉
socle, prime radical	C₂²×C₃×C₁₄₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7152 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₁₆×C₁₄₉, C₃×C₄×C₈×C₁₄₉, C₂²×C₃×C₈×C₁₄₉, …
maximal normal subgroup of	C₂×C₃×C₁₆×C₁₄₉, C₃×C₄×C₈×C₁₄₉, C₂²×C₃×C₈×C₁₄₉, …
maximal quotient of	C₂×C₃×C₁₆×C₁₄₉, C₃×C₄×C₈×C₁₄₉, C₂²×C₃×C₈×C₁₄₉, …
automorphism group of	C₇×C₁₁₉₃, C₉×C₁₁₉₃
outer automorphism group of	C₇×C₁₁₉₃, C₉×C₁₁₉₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.