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C₁₉×C₃⋊Dic₃×C₄₇ #44565291

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

Aliases

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

Splittings

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

Subgroups

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

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 32148

Conjugacy classes & character table

10716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 51);