Finite Group Databasebeta

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C₂×C₃×C₂₇×C₈₉ #72192593

order	14418
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 28512
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₂×C₃×C₂₇×C₈₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃²×C₈₉
socle, prime radical	C₂×C₃²×C₈₉	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14418 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₂₇×C₈₉, C₂²×C₃×C₂₇×C₈₉
maximal normal subgroup of	C₃×C₄×C₂₇×C₈₉, C₂²×C₃×C₂₇×C₈₉
maximal quotient of	C₃×C₄×C₂₇×C₈₉, C₂²×C₃×C₂₇×C₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.