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C₃×(C₄₉⋊C₃)⋊D₁₃ #26039394

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×(C₄₉⋊C₃)⋊D₁₃
unambiguous semidirect product	(C₄₉⋊C₃)⋊(C₃×D₁₃)

Splittings

Fitting	C₃×C₁₃×C₄₉ ⋊ C₂×C₃
derived, Hall	C₁₃×C₄₉ ⋊ C₂×C₃²
Hall	C₃×C₁₃×C₄₉⋊C₃ ⋊ C₂
Hall	D₆₃₇ ⋊ C₃²
Hall	C₃×C₄₉⋊C₃ ⋊ D₁₃
Sylow	C₄₉ ⋊ C₃²×D₁₃
Sylow	C₁₃ ⋊ C₃×D₄₉⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	(C₄₉⋊C₃)⋊D₁₃
commutator, cosocle, hypocenter	C₁₃×C₄₉	C₂×C₃²
Frattini	C₇	C₃×ΓL(1,𝔽₈)⋊D₁₃
Fitting	C₃×C₁₃×C₄₉	C₂×C₃
socle	C₃×C₇×C₁₃	AGL(1,𝔽₇)
LCS	G ▷ C₁₃×C₄₉
UCS	C₁ ◁ C₃

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

384 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₁₃×D₄₉⋊C₃, D₃×(C₄₉⋊C₃)⋊D₁₃, (C₃⋊(D₄₉⋊C₃))⋊D₁₃, …
maximal normal subgroup of	C₃×D₁₃×D₄₉⋊C₃, D₃×(C₄₉⋊C₃)⋊D₁₃, (C₃⋊(D₄₉⋊C₃))⋊D₁₃, …
maximal quotient of	C₃×(C₄₉⋊C₃)⋊Dic₁₃, C₂×C₃×(C₄₉⋊C₃)⋊D₁₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 37);