Finite Group Databasebeta

← Prev (#72183287) Next (#72183289) →

C₂×C₃×C₁₉×C₃₂ #72183288

order	3648
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2304
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂×C₃×C₁₉×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂²×C₃×C₁₉
socle, prime radical	C₂²×C₃×C₁₉	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

68 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3648 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₁₉×C₆₄, C₃×C₄×C₁₉×C₃₂, C₂²×C₃×C₁₉×C₃₂, …
maximal normal subgroup of	C₂×C₃×C₁₉×C₆₄, C₃×C₄×C₁₉×C₃₂, C₂²×C₃×C₁₉×C₃₂, …
maximal quotient of	C₂×C₃×C₁₉×C₆₄, C₃×C₄×C₁₉×C₃₂, C₂²×C₃×C₁₉×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.