Finite Group Databasebeta

← Prev (#63337) Next (#63339) →

Cayley diagram

C3×D47 #63338

order282
isoclinismisoclinic class of D47
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D47
unambiguous semidirect productC47⋊(C2×C3)

Splittings

Fitting, socle, HallC3×C47 ⋊ C2
derived, SylowC47 ⋊ C2×C3

Subgroups

subgroupG/H
center, hypercenterC3D47
commutator, cosocle, hypocenterC47C2×C3
FrattiniC1G
Fitting, socleC3×C47C2
LCSG ▷ C47
UCSC1 ◁ C3

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 141

A minimal faithful permutation representation — 2 generators on 50 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)(45,46)(47,48)(49,50);(4,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6)

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D47, C2×C3×D47, C9×D47, …
maximal normal subgroup ofD3×D47, C2×C3×D47, C9×D47, …
maximal quotient ofC3×Dic47, C2×C3×D47, C9×D47, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(282, 2);