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D₃×(C₁₃⋊C₃)⋊D₁₃ #20258909

order	6084
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×(C₁₃⋊C₃)⋊D₁₃
unambiguous semidirect product	(D₃×C₁₃⋊C₃)⋊D₁₃

Splittings

Fitting, socle, derived	C₃×C₁₃² ⋊ C₂²×C₃
Hall	C₃×C₁₃×C₁₃⋊C₃ ⋊ C₂²
Sylow	C₁₃² ⋊ C₂×C₃×D₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃²	C₂²×C₃
LCS	G ▷ C₃×C₁₃²
UCS	C₁

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×(C₁₃⋊C₃)⋊D₁₃, D₁₅×(C₁₃⋊C₃)⋊D₁₃, D₃×C₅⋊((C₁₃⋊C₃)⋊D₁₃), …
maximal normal subgroup of	C₅×D₃×(C₁₃⋊C₃)⋊D₁₃
maximal quotient of	C₅×D₃×(C₁₃⋊C₃)⋊D₁₃, D₁₅×(C₁₃⋊C₃)⋊D₁₃, D₃×C₅⋊((C₁₃⋊C₃)⋊D₁₃), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6084, 216);