Finite Group Databasebeta

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C₂×C₃²×C₉×C₆₇ #72189404

order	10854
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1539648
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₂×C₃²×C₉×C₆₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃³×C₆₇
socle, prime radical	C₂×C₃³×C₆₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10854 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₉×C₆₇, C₂²×C₃²×C₉×C₆₇, C₂×C₃²×C₂₇×C₆₇, …
maximal normal subgroup of	C₃²×C₄×C₉×C₆₇, C₂²×C₃²×C₉×C₆₇, C₂×C₃²×C₂₇×C₆₇, …
maximal quotient of	C₃²×C₄×C₉×C₆₇, C₂²×C₃²×C₉×C₆₇, C₂×C₃²×C₂₇×C₆₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.