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C₂³×C₃²×C₇×C₁₉ #72188291

order	9576
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 870912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂³×C₃²×C₇×C₁₉

Subgroups

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

384 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9576 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃²×C₄×C₇×C₁₉, C₂⁴×C₃²×C₇×C₁₉, C₂³×C₃×C₇×C₉×C₁₉, …
maximal normal subgroup of	C₂²×C₃²×C₄×C₇×C₁₉, C₂⁴×C₃²×C₇×C₁₉, C₂³×C₃×C₇×C₉×C₁₉, …
maximal quotient of	C₂²×C₃²×C₄×C₇×C₁₉, C₂⁴×C₃²×C₇×C₁₉, C₂³×C₃×C₇×C₉×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.