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C₂²×C₃×C₁₉×C₃₂ #72186336

order	7296
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 55296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₃×C₁₉×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂³×C₃×C₁₉
socle, prime radical	C₂³×C₃×C₁₉	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

240 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	C₂²×C₃×C₁₉×C₆₄, C₂×C₃×C₄×C₁₉×C₃₂, C₂³×C₃×C₁₉×C₃₂, …
maximal normal subgroup of	C₂²×C₃×C₁₉×C₆₄, C₂×C₃×C₄×C₁₉×C₃₂, C₂³×C₃×C₁₉×C₃₂, …
maximal quotient of	C₂²×C₃×C₁₉×C₆₄, C₂×C₃×C₄×C₁₉×C₃₂, C₂³×C₃×C₁₉×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.