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C₁₃×C₁₉×Dic₃₉ #50310263

order	38532
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₁₉×Dic₃₉
unambiguous semidirect product	C₃⋊(C₁₃×C₁₉×Dic₁₃)

Splittings

derived	C₃×C₁₃ ⋊ C₄×C₁₃×C₁₉
Hall	C₃×C₁₃²×C₁₉ ⋊ C₄
Hall	C₁₃²×C₁₉ ⋊ Dic₃
Hall	C₃×C₁₃² ⋊ C₄×C₁₉
Sylow	C₁₃² ⋊ Dic₃×C₁₉
Hall	C₃×C₁₉ ⋊ C₁₃×Dic₁₃
Sylow	C₃ ⋊ C₁₃×C₁₉×Dic₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₉	D₃₉
commutator, hypocenter	C₃×C₁₃	C₄×C₁₃×C₁₉
Frattini	C₂	C₁₃×C₁₉×D₃₉
Fitting, socle, prime radical	C₂×C₃×C₁₃²×C₁₉	C₂
cosocle	C₂×C₃×C₁₃	C₂×C₁₃×C₁₉
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₁₃×C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2964

Conjugacy classes & character table

10374 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38532, 145);