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C₂⁷×C₃×C₁₉ #72186348

order	7296
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5898599745454080
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²¹

Aliases

C₂⁷×C₃×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

116848 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	C₂⁶×C₃×C₄×C₁₉, C₂⁸×C₃×C₁₉, C₂⁷×C₉×C₁₉, …
maximal normal subgroup of	C₂⁶×C₃×C₄×C₁₉, C₂⁸×C₃×C₁₉, C₂⁷×C₉×C₁₉, …
maximal quotient of	C₂⁶×C₃×C₄×C₁₉, C₂⁸×C₃×C₁₉, C₂⁷×C₉×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.