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C₃⋊D₃×C₁₉×C₄₉ #30660554

order	16758
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₄₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃⋊D₃×C₁₉×C₄₉
unambiguous semidirect product	C₃⋊(D₃×C₁₉×C₄₉)

Splittings

Fitting, Hall	C₃²×C₁₉×C₄₉ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₁₉×C₄₉
Hall	C₃²×C₄₉ ⋊ C₂×C₁₉
Hall	C₃²×C₁₉ ⋊ C₂×C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₄₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₁₉×C₄₉
Frattini	C₇	C₇×C₃⋊D₃×C₁₉
Fitting	C₃²×C₁₉×C₄₉	C₂
socle	C₃²×C₇×C₁₉	C₂×C₇
prime radical	C₇×C₃⋊D₃×C₁₉	C₇
cosocle	C₃²×C₇	C₂×C₇×C₁₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₉×C₄₉

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8379

Conjugacy classes & character table

5586 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃⋊D₃×D₁₉×C₄₉, C₃⋊D₃×C₁₉×D₄₉, C₃⋊D₃×D₉₃₁, …
maximal normal subgroup of	C₃⋊D₃×D₁₉×C₄₉, C₃⋊D₃×C₁₉×D₄₉, C₃⋊D₃×D₉₃₁, …
maximal quotient of	C₁₉×C₃⋊Dic₃×C₄₉, C₂×C₃⋊D₃×C₁₉×C₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 81);