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Cayley diagram

C5×D41 #88014

order410
isoclinismisoclinic class of D41
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D41

Splittings

Fitting, socle, HallC5×C41 ⋊ C2
derived, SylowC41 ⋊ C2×C5

Subgroups

subgroupG/H
center, hypercenterC5D41
commutator, cosocle, hypocenterC41C2×C5
FrattiniC1G
Fitting, socleC5×C41C2
LCSG ▷ C41
UCSC1 ◁ C5

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 205

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2,3,4,5)(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)(45,46);(6,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8)

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#4223, #11717964, D5×D41, …
maximal normal subgroup ofC5×#4223, #11717964, D5×D41, …
maximal quotient ofC5×Dic41, C2×C5×D41, C3×C5×D41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(410, 4);