Finite Group Databasebeta

← Prev (#92509) Next (#92511) →

Cayley diagram

D3×C83 #92510

order498
isoclinismisoclinic class of D3
automorphismAut(G) = C2×D3×C41 (order 492) · Inn(G) = D3 · Out(G) = C2×C41
homologyAbelianization (H1) = C2×C83 · Schur multiplier (H2) = C1

Aliases

direct productD3×C83
unambiguous semidirect productC3⋊(C2×C83)

Splittings

Fitting, socle, HallC3×C83 ⋊ C2
derived, SylowC3 ⋊ C2×C83

Subgroups

subgroupG/H
center, hypercenterC83D3
commutator, cosocle, hypocenterC3C2×C83
FrattiniC1G
Fitting, socleC3×C83C2
LCSG ▷ C3
UCSC1 ◁ C83

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 86
transitive degreeμt(G) = 249

A minimal faithful permutation representation — 2 generators on 86 points:

(2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86);(1,2,3)

Conjugacy classes & character table

249 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D83, C2×D3×C83, D9×C83, …
maximal normal subgroup ofD3×D83, C2×D3×C83, C3×D3×C83, …
maximal quotient ofDic3×C83, C2×D3×C83, D9×C83, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(498, 1);