Finite Group Databasebeta

← Prev (#72188440) Next (#72188442) →

C₂³×C₄×C₁₆×C₁₉ #72188441

order	9728
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3170893824
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

C₂³×C₄×C₁₆×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂⁵×C₁₉
socle, prime radical	C₂⁵×C₁₉	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

6276 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9728 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₄×C₁₉×C₃₂, C₂³×C₈×C₁₆×C₁₉, C₂²×C₄²×C₁₆×C₁₉, …
maximal normal subgroup of	C₂³×C₄×C₁₉×C₃₂, C₂³×C₈×C₁₆×C₁₉, C₂²×C₄²×C₁₆×C₁₉, …
maximal quotient of	C₂³×C₄×C₁₉×C₃₂, C₂³×C₈×C₁₆×C₁₉, C₂²×C₄²×C₁₆×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.