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C₂²×C₃³×C₄×C₂₉ #72190877

order	12528
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 60383232
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃³

Aliases

abelian	C₂²×C₃³×C₄×C₂₉
multiplicative	(ℤ/21987)ˣ, (ℤ/43974)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃³×C₂₉
socle, prime radical	C₂³×C₃³×C₂₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

1512 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	C₂²×C₃³×C₈×C₂₉, C₂×C₃³×C₄²×C₂₉, C₂³×C₃³×C₄×C₂₉
maximal normal subgroup of	C₂²×C₃³×C₈×C₂₉, C₂×C₃³×C₄²×C₂₉, C₂³×C₃³×C₄×C₂₉
maximal quotient of	C₂²×C₃³×C₈×C₂₉, C₂×C₃³×C₄²×C₂₉, C₂³×C₃³×C₄×C₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.