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D₁₃₉⋊C₂₃ #20264153

order	6394
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	D₁₃₉⋊C₂₃
unambiguous semidirect product	(C₁₃₉⋊C₂₃)⋊C₂

Splittings

Fitting, socle, derived, Sylow	C₁₃₉ ⋊ C₂×C₂₃
Hall	C₁₃₉⋊C₂₃ ⋊ C₂
Hall	D₁₃₉ ⋊ C₂₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃₉	C₂×C₂₃
LCS	G ▷ C₁₃₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,23,139|c^a=c^138,c^b=c^64

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₁₃₉⋊C₂₃, C₃×D₁₃₉⋊C₂₃, C₃⋊(D₁₃₉⋊C₂₃), …
maximal normal subgroup of	C₂×D₁₃₉⋊C₂₃, C₃×D₁₃₉⋊C₂₃, AGL(1,𝔽₁₃₉), …
maximal quotient of	Dic₁₃₉⋊C₂₃, C₂×D₁₃₉⋊C₂₃, C₃×D₁₃₉⋊C₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6394, 1);