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C₃²×C₄²×C₅×C₁₉ #72191889

order	13680
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 331776
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄

Aliases

abelian	C₃²×C₄²×C₅×C₁₉
multiplicative	(ℤ/13969)ˣ, (ℤ/27938)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃²×C₅×C₁₉
socle, prime radical	C₂²×C₃²×C₅×C₁₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₅×C₈×C₁₉, C₂×C₃²×C₄²×C₅×C₁₉
maximal normal subgroup of	C₃²×C₄×C₅×C₈×C₁₉, C₂×C₃²×C₄²×C₅×C₁₉
maximal quotient of	C₃²×C₄×C₅×C₈×C₁₉, C₂×C₃²×C₄²×C₅×C₁₉
automorphism group of	C₆₁×C₂₂₉
outer automorphism group of	C₆₁×C₂₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.