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C₂×C₄×C₅×C₈×C₁₉ #72185261

order	6080
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 147456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian	C₂×C₄×C₅×C₈×C₁₉
multiplicative	(ℤ/11415)ˣ, (ℤ/12176)ˣ, (ℤ/15220)ˣ, (ℤ/22830)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂³×C₅×C₁₉
socle, prime radical	C₂³×C₅×C₁₉	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₅×C₁₆×C₁₉, C₂×C₅×C₈²×C₁₉, C₄²×C₅×C₈×C₁₉, …
maximal normal subgroup of	C₂×C₄×C₅×C₁₆×C₁₉, C₂×C₅×C₈²×C₁₉, C₄²×C₅×C₈×C₁₉, …
maximal quotient of	C₂×C₄×C₅×C₁₆×C₁₉, C₂×C₅×C₈²×C₁₉, C₄²×C₅×C₈×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.