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C₂×C₃²×C₆₄₁ #26040396

order	11538
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 30720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₂×C₃²×C₆₄₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11538 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃⋊Dic₁₉₂₃, C₃⋊Dic₃×C₆₄₁, C₃×Dic₁₉₂₃, …
socle of	C₃²×C₄×C₆₄₁, C₃⋊Dic₁₉₂₃, C₃⋊Dic₃×C₆₄₁, …
maximal subgroup of	C₃²×C₄×C₆₄₁, C₃⋊Dic₁₉₂₃, C₃⋊Dic₃×C₆₄₁, …
maximal normal subgroup of	C₃²×C₄×C₆₄₁, C₃⋊Dic₁₉₂₃, C₃⋊Dic₃×C₆₄₁, …
maximal quotient of	C₃²×C₄×C₆₄₁, C₂²×C₃²×C₆₄₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11538, 5);