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C₂²×C₉²×C₁₉ #72185355

order	6156
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 419904
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₉

Aliases

abelian	C₂²×C₉²×C₁₉
multiplicative	(ℤ/9747)ˣ, (ℤ/19494)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃²	C₂²×C₃²×C₁₉
socle, prime radical	C₂²×C₃²×C₁₉	C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

230 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6156 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₉²×C₁₉, C₂³×C₉²×C₁₉, C₂²×C₉×C₁₉×C₂₇, …
maximal normal subgroup of	C₂×C₄×C₉²×C₁₉, C₂³×C₉²×C₁₉, C₂²×C₉×C₁₉×C₂₇, …
maximal quotient of	C₂×C₄×C₉²×C₁₉, C₂³×C₉²×C₁₉, C₂²×C₉×C₁₉×C₂₇, …
automorphism group of	C₂₇×C₃₆₁, C₂×C₂₇×C₃₆₁
outer automorphism group of	C₂₇×C₃₆₁, C₂×C₂₇×C₃₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.