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(C₄₉⋊C₉)⋊D₁₃ #26039366

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product

(C₄₉⋊C₉)⋊D₁₃

Splittings

derived, Hall	C₁₃×C₄₉ ⋊ C₂×C₉
Hall	C₁₃×C₄₉⋊C₉ ⋊ C₂
Hall	D₆₃₇ ⋊ C₉
Hall	C₄₉⋊C₉ ⋊ D₁₃
Sylow	C₄₉ ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ D₄₉⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	(C₄₉⋊C₃)⋊D₁₃
commutator, hypocenter	C₁₃×C₄₉	C₂×C₉
Frattini	C₃×C₇	ΓL(1,𝔽₈)⋊D₁₃
Fitting, cosocle	C₃×C₁₃×C₄₉	C₂×C₃
socle	C₃×C₇×C₁₃	AGL(1,𝔽₇)
prime radical	C₃×D₆₃₇	C₃
LCS	G ▷ C₁₃×C₄₉
UCS	C₁ ◁ C₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,7,13,3,7|b^3=e,c^7=f^6,c^a=c^6f,d^a=d^12,f^a=f^6,c^b=c^2f^3,f^b=f^2

Conjugacy classes & character table

384 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₃×D₄₉⋊C₉, C₂×(C₄₉⋊C₉)⋊D₁₃
maximal normal subgroup of	D₁₃×D₄₉⋊C₉, C₂×(C₄₉⋊C₉)⋊D₁₃
maximal quotient of	(C₄₉⋊C₉)⋊Dic₁₃, C₂×(C₄₉⋊C₉)⋊D₁₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 9);