Finite Group Databasebeta

← Prev (#72186339) Next (#72186341) →

C₂³×C₃×C₁₆×C₁₉ #72186340

order	7296
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3096576
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×C₃×C₁₆×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂⁴×C₃×C₁₉
socle, prime radical	C₂⁴×C₃×C₁₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

880 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	C₂³×C₃×C₁₉×C₃₂, C₂²×C₃×C₄×C₁₆×C₁₉, C₂⁴×C₃×C₁₆×C₁₉, …
maximal normal subgroup of	C₂³×C₃×C₁₉×C₃₂, C₂²×C₃×C₄×C₁₆×C₁₉, C₂⁴×C₃×C₁₆×C₁₉, …
maximal quotient of	C₂³×C₃×C₁₉×C₃₂, C₂²×C₃×C₄×C₁₆×C₁₉, C₂⁴×C₃×C₁₆×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.