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C₂×C₄×C₉×C₁₄₉ #72189270

order	10728
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7104
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₉×C₁₄₉
multiplicative	(ℤ/13415)ˣ, (ℤ/26830)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃×C₁₄₉
socle, prime radical	C₂²×C₃×C₁₄₉	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10728 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₉×C₁₄₉, C₄²×C₉×C₁₄₉, C₂²×C₄×C₉×C₁₄₉, …
maximal normal subgroup of	C₂×C₈×C₉×C₁₄₉, C₄²×C₉×C₁₄₉, C₂²×C₄×C₉×C₁₄₉, …
maximal quotient of	C₂×C₈×C₉×C₁₄₉, C₄²×C₉×C₁₄₉, C₂²×C₄×C₉×C₁₄₉, …
automorphism group of	C₅×C₂₆₈₃
outer automorphism group of	C₅×C₂₆₈₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.