Finite Group Databasebeta

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Dic₃×C₄₇×C₁₉⋊C₃ #44565285

order	32148
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₄₇×C₁₉⋊C₃
unambiguous semidirect product	C₃⋊(C₄×C₄₇×C₁₉⋊C₃)
unambiguous semidirect product	(Dic₃×C₁₉)⋊(C₃×C₄₇)
unambiguous semidirect product	(Dic₃×C₁₉×C₄₇)⋊C₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₇	D₃×C₁₉⋊C₃
commutator, hypocenter	C₃×C₁₉	C₃×C₄×C₄₇
Frattini	C₂	D₃×C₄₇×C₁₉⋊C₃
Fitting, socle	C₂×C₃×C₁₉×C₄₇	C₂×C₃
prime radical	C₂×C₃×C₄₇×C₁₉⋊C₃	C₂
cosocle	C₂×C₃×C₁₉	C₂×C₃×C₄₇
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₄₇

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10716

Conjugacy classes & character table

2538 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 45);