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C₂³×C₇×C₉×C₁₉ #72188290

order	9576
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 108864
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

C₂³×C₇×C₉×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂³×C₃×C₇×C₁₉
socle, prime radical	C₂³×C₃×C₇×C₁₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

192 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×C₄×C₇×C₉×C₁₉, C₂⁴×C₇×C₉×C₁₉, C₂³×C₇×C₁₉×C₂₇, …
maximal normal subgroup of	C₂²×C₄×C₇×C₉×C₁₉, C₂⁴×C₇×C₉×C₁₉, C₂³×C₇×C₁₉×C₂₇, …
maximal quotient of	C₂²×C₄×C₇×C₉×C₁₉, C₂⁴×C₇×C₉×C₁₉, C₂³×C₇×C₁₉×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.