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C₁₃×(C₃⋊D₃)⋊D₁₃ #20258965

order	6084
isoclinism	isoclinic class of (C₃⋊D₃)⋊D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×(C₃⋊D₃)⋊D₁₃
unambiguous semidirect product	(C₃⋊D₃)⋊(C₁₃×D₁₃)
unambiguous semidirect product	D₃₉⋊(D₃×C₁₃)

Splittings

Fitting, socle, Hall	C₃²×C₁₃² ⋊ C₂²
derived	C₃²×C₁₃ ⋊ C₂²×C₁₃
Sylow	C₁₃² ⋊ D₃²
Sylow	C₃² ⋊ C₂×C₁₃×D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	(C₃⋊D₃)⋊D₁₃
commutator, hypocenter	C₃²×C₁₃	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃²	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₁₃

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

585 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×C₁₃×(C₃⋊D₃)⋊D₁₃, C₁₃×D₃₉⋊D₁₅, C₁₃×(C₃⋊D₃)⋊D₆₅
maximal normal subgroup of	C₅×C₁₃×(C₃⋊D₃)⋊D₁₃
maximal quotient of	C₅×C₁₃×(C₃⋊D₃)⋊D₁₃, C₁₃×D₃₉⋊D₁₅, C₁₃×(C₃⋊D₃)⋊D₆₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6084, 272);