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Cayley diagram

C3×D41 #6929

order246
isoclinismisoclinic class of D41
automorphismAut(G) = C2×AGL(1,𝔽41) (order 3280) · Inn(G) = D41 · Out(G) = C2×C4×C5
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D41
unambiguous semidirect productC41⋊(C2×C3)

Splittings

Fitting, socle, HallC3×C41 ⋊ C2
derived, SylowC41 ⋊ C2×C3

Subgroups

subgroupG/H
center, hypercenterC3D41
commutator, cosocle, hypocenterC41C2×C3
FrattiniC1G
Fitting, socleC3×C41C2
LCSG ▷ C41
UCSC1 ◁ C3

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 123

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3)(5,6)(7,8)(9,10)(11,12)(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)(41,42)(43,44);(4,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#4223, C3⋊#4223, D3×D41, …
maximal normal subgroup ofC3×#4223, C3⋊#4223, D3×D41, …
maximal quotient ofC3×Dic41, C2×C3×D41, C9×D41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(246, 2);