Finite Group Databasebeta

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C₃×Dic₃×C₁₉×C₄₇ #44565295

order	32148
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉×C₄₇	D₃
commutator, hypocenter	C₃	C₃×C₄×C₁₉×C₄₇
Frattini	C₂	C₃×D₃×C₁₉×C₄₇
Fitting, socle, prime radical	C₂×C₃²×C₁₉×C₄₇	C₂
cosocle	C₂×C₃	C₂×C₃×C₁₉×C₄₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₁₉×C₄₇

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10716

Conjugacy classes & character table

16074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 55);