Finite Group Databasebeta

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C₂×C₃×C₄×C₉×C₂₇ #72185076

order	5832
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 11337408
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃²×C₉

Aliases

C₂×C₃×C₄×C₉×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₉	C₂²×C₃³
socle, prime radical	C₂²×C₃³	C₂×C₃×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

1616 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5832 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₉×C₂₇, C₃×C₄²×C₉×C₂₇, C₂²×C₃×C₄×C₉×C₂₇, …
maximal normal subgroup of	C₂×C₃×C₈×C₉×C₂₇, C₃×C₄²×C₉×C₂₇, C₂²×C₃×C₄×C₉×C₂₇, …
maximal quotient of	C₂×C₃×C₈×C₉×C₂₇, C₃×C₄²×C₉×C₂₇, C₂²×C₃×C₄×C₉×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.