Finite Group Databasebeta

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C₂×C₃×C₄×C₁₆×C₁₉ #72186338

order	7296
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×C₃×C₄×C₁₆×C₁₉
multiplicative	(ℤ/11679)ˣ, (ℤ/14656)ˣ, (ℤ/15572)ˣ, (ℤ/23358)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂³×C₃×C₁₉
socle, prime radical	C₂³×C₃×C₁₉	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7296 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₁₉×C₃₂, C₂×C₃×C₈×C₁₆×C₁₉, C₃×C₄²×C₁₆×C₁₉, …
maximal normal subgroup of	C₂×C₃×C₄×C₁₉×C₃₂, C₂×C₃×C₈×C₁₆×C₁₉, C₃×C₄²×C₁₆×C₁₉, …
maximal quotient of	C₂×C₃×C₄×C₁₉×C₃₂, C₂×C₃×C₈×C₁₆×C₁₉, C₃×C₄²×C₁₆×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.