C₃×C₉×D₂₉ #13095808

order	1566
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₉×D₂₉
unambiguous semidirect product	C₂₉⋊(C₂×C₃×C₉)

Splittings

Fitting, Hall	C₃×C₉×C₂₉ ⋊ C₂
derived, Sylow	C₂₉ ⋊ C₂×C₃×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₉	D₂₉
commutator, hypocenter	C₂₉	C₂×C₃×C₉
Frattini	C₃	C₃²×D₂₉
Fitting	C₃×C₉×C₂₉	C₂
socle	C₃²×C₂₉	C₂×C₃
prime radical	C₃²×D₂₉	C₃
cosocle	C₃×C₂₉	C₂×C₃²
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₃×C₉

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 783

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(4,5,6,7,8,9,10,11,12)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1566, 5);

C3×C9×D29 #13095808