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C₃×C₁₉×Dic₁₄₁ #44565294

order	32148
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₉×Dic₁₄₁
unambiguous semidirect product	C₃⋊(C₃×C₁₉×Dic₄₇)
unambiguous semidirect product	C₄₇⋊(C₃×Dic₃×C₁₉)

Splittings

derived	C₃×C₄₇ ⋊ C₃×C₄×C₁₉
Hall	C₃²×C₁₉×C₄₇ ⋊ C₄
Hall	C₁₉×C₄₇ ⋊ C₃×Dic₃
Hall	C₃²×C₄₇ ⋊ C₄×C₁₉
Hall	C₃²×C₁₉ ⋊ Dic₄₇
Sylow	C₄₇ ⋊ C₃×Dic₃×C₁₉
Sylow	C₃² ⋊ C₁₉×Dic₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₁₄₁
commutator, hypocenter	C₃×C₄₇	C₃×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×D₁₄₁
Fitting, socle, prime radical	C₂×C₃²×C₁₉×C₄₇	C₂
cosocle	C₂×C₃×C₄₇	C₂×C₃×C₁₉
LCS	G ▷ C₃×C₄₇
UCS	C₁ ◁ C₂×C₃×C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10716

Conjugacy classes & character table

8208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 54);