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C₃×C₄²×C₉×C₂₉ #72190872

order	12528
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 290304
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄

Aliases

abelian	C₃×C₄²×C₉×C₂₉
multiplicative	(ℤ/12913)ˣ, (ℤ/25826)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂²×C₃²×C₂₉
socle, prime radical	C₂²×C₃²×C₂₉	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

300 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₈×C₉×C₂₉, C₂×C₃×C₄²×C₉×C₂₉
maximal normal subgroup of	C₃×C₄×C₈×C₉×C₂₉, C₂×C₃×C₄²×C₉×C₂₉
maximal quotient of	C₃×C₄×C₈×C₉×C₂₉, C₂×C₃×C₄²×C₉×C₂₉
automorphism group of	C₃₇×C₃₄₉
outer automorphism group of	C₃₇×C₃₄₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.