Finite Group Databasebeta

← Prev (#32915282) Next (#32915284) →

A5×C103⋊C3 #32915283

order18540
automorphism?
homologyAbelianization (H1) = C3 · Schur multiplier (H2) = C2

Aliases

direct productA5×C103⋊C3
unambiguous semidirect productC103⋊(C3×A5)
unambiguous semidirect product(A5×C103)⋊C3

Splittings

Fitting, SylowC103 ⋊ C3×A5
socle, derivedA5×C103 ⋊ C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, socle, hypocenterA5×C103C3
Fitting, cosocleC103C3×A5
LCSG ▷ A5×C103
UCSC1

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 108
transitive degreeμt(G) = 515

A minimal faithful permutation representation — 2 generators on 108 points:

(1,3,7,13,24,41,62,83,69,27,45,40,21,4,8,15,28,47,68,88,82,58,18,33,52,71,90,101,66,85,96,55,76,94,93,53,72,81,65,25,42,63,84,99,91,51,16,29,39,6,12,22,38,59,80,48,14,26,23,11,20,36,57,78,89,46,67,61,37,9,17,31,49,70,87,100,98,79,34,54,74,75,92,97,86,44,64,77,95,103,102,73,32,50,60,43,2,5,10,19,35,56,30)(104,105,106,107,108);(1,2,4)(3,6,11)(5,9,16)(8,14,25)(10,18,32)(12,21,29)(13,23,39)(15,27,44)(17,30,42)(19,34,53)(20,26,43)(22,37,50)(24,40,60)(28,46,66)(31,48,64)(33,51,63)(35,55,75)(36,45,65)(38,58,72)(41,61,81)(47,68,87)(49,69,85)(52,56,77)(54,73,84)(57,67,86)(59,79,92)(62,82,97)(70,89,100)(71,80,96)(74,91,95)(76,93,99)(78,88,101)(83,98,90)(94,102,103)(104,107,105,106,108)

Conjugacy classes & character table

185 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18540, 131);