Finite Group Databasebeta

← Prev (#27189123) Next (#27189125) →

D3×C7×D31⋊C5 #27189124

order13020
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D31⋊C5
unambiguous semidirect productD31⋊(C5×D3×C7)
unambiguous semidirect product(D3×D31)⋊(C5×C7)
unambiguous semidirect product(C3×D31⋊C5)⋊(C2×C7)
unambiguous semidirect product(D3×ΓL(1,𝔽32))⋊(C2×C7)
unambiguous semidirect product(C3⋊(D31⋊C5))⋊(C2×C7)
unambiguous semidirect product(D3×C7×D31)⋊C5

Splittings

Fitting, socle, HallC3×C7×C31 ⋊ C22×C5
derived, HallC3×C31 ⋊ C22×C5×C7
HallC3×C7×ΓL(1,𝔽32) ⋊ C22
HallD3×C7×D31 ⋊ C5
HallC7×ΓL(1,𝔽32) ⋊ C2×D3
HallC3×ΓL(1,𝔽32) ⋊ C22×C7
HallD3×D31 ⋊ C5×C7
HallC7×C31 ⋊ C2×C5×D3
HallΓL(1,𝔽32) ⋊ C2×D3×C7
SylowC31 ⋊ C2×C5×D3×C7
HallC3×C7 ⋊ C2×D31⋊C5
SylowC3 ⋊ C2×C7×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC7D3×D31⋊C5
commutator, cosocle, hypocenterC3×C31C22×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C31C22×C5
LCSG ▷ C3×C31
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 651

A minimal faithful permutation representation — 2 generators on 41 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 91);