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C₂×C₉×C₁₆×C₂₉ #72187258

order	8352
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5376
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₉×C₁₆×C₂₉
multiplicative	(ℤ/8891)ˣ, (ℤ/12531)ˣ, (ℤ/16708)ˣ, (ℤ/17782)ˣ, (ℤ/25062)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂²×C₃×C₂₉
socle, prime radical	C₂²×C₃×C₂₉	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₉×C₂₉×C₃₂, C₄×C₉×C₁₆×C₂₉, C₂²×C₉×C₁₆×C₂₉, …
maximal normal subgroup of	C₂×C₉×C₂₉×C₃₂, C₄×C₉×C₁₆×C₂₉, C₂²×C₉×C₁₆×C₂₉, …
maximal quotient of	C₂×C₉×C₂₉×C₃₂, C₄×C₉×C₁₆×C₂₉, C₂²×C₉×C₁₆×C₂₉, …
automorphism group of	C₁₇×C₅₂₃, C₃×C₄₁₇₇
outer automorphism group of	C₁₇×C₅₂₃, C₃×C₄₁₇₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.