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C₄²×C₉×C₂₇ #72183457

order	3888
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 839808
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄×C₉

Aliases

abelian	C₄²×C₉×C₂₇
multiplicative	(ℤ/4033)ˣ, (ℤ/8066)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃×C₉	C₂²×C₃²
socle, prime radical	C₂²×C₃²	C₂²×C₃×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

540 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3888 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₈×C₉×C₂₇, C₂×C₄²×C₉×C₂₇, C₄²×C₉×C₈₁, …
maximal normal subgroup of	C₄×C₈×C₉×C₂₇, C₂×C₄²×C₉×C₂₇, C₄²×C₉×C₈₁, …
maximal quotient of	C₄×C₈×C₉×C₂₇, C₂×C₄²×C₉×C₂₇, C₄²×C₉×C₈₁, …
automorphism group of	C₃₇×C₁₀₉, C₂×C₃₇×C₁₀₉
outer automorphism group of	C₃₇×C₁₀₉, C₂×C₃₇×C₁₀₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.