Finite Group Databasebeta

← Prev (#44501414) Next (#44501416) →

C5×D7×D219 #44501415

order30660
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D7×D219
unambiguous semidirect product(C3×D7)⋊(C5×D73)
unambiguous semidirect product(D7×C73)⋊(C5×D3)

Splittings

Fitting, socle, HallC3×C5×C7×C73 ⋊ C22
derived, HallC3×C7×C73 ⋊ C22×C5
HallC5×C7×C73 ⋊ C2×D3
HallC3×C5×C73 ⋊ C2×D7
HallC7×C73 ⋊ C2×C5×D3
HallC5×C73 ⋊ D3×D7
HallC3×C73 ⋊ C2×C5×D7
HallC3×C5×C7 ⋊ C2×D73
SylowC73 ⋊ C5×D3×D7
HallC5×C7 ⋊ C2×D219
HallC3×C7 ⋊ C2×C5×D73
HallC3×C5 ⋊ D7×D73
SylowC7 ⋊ C2×C5×D219
SylowC3 ⋊ C5×D7×D73

Subgroups

subgroupG/H
center, hypercenterC5D7×D219
commutator, cosocle, hypocenterC3×C7×C73C22×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C73C22
LCSG ▷ C3×C7×C73
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 88
transitive degreeμt(G) = 7665

A minimal faithful permutation representation — 2 generators on 88 points:

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

Conjugacy classes & character table

2775 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 178);