Finite Group Databasebeta

← Prev (#34084405) Next (#34084407) →

C2×C5×D969 #34084406

order19380
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D969
unambiguous semidirect product(C2×C3)⋊(C5×D323)
unambiguous semidirect product(C2×C17)⋊(C5×D57)
unambiguous semidirect product(C2×C19)⋊(C5×D51)

Splittings

Fitting, socleC2×C3×C5×C17×C19 ⋊ C2
derived, HallC3×C17×C19 ⋊ C22×C5
HallC3×C5×C17×C19 ⋊ C22
HallC5×C17×C19 ⋊ C2×D3
HallC17×C19 ⋊ C2×C5×D3
HallC3×C5×C19 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D19
HallC5×C19 ⋊ C2×D51
HallC5×C17 ⋊ C2×D57
HallC3×C19 ⋊ C2×C5×D17
HallC3×C17 ⋊ C2×C5×D19
SylowC19 ⋊ C2×C5×D51
SylowC17 ⋊ C2×C5×D57
HallC3×C5 ⋊ C2×D323
SylowC3 ⋊ C2×C5×D323

Subgroups

subgroupG/H
center, hypercenterC2×C5D969
commutator, cosocle, hypocenterC3×C17×C19C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C19C2
LCSG ▷ C3×C17×C19
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 9690

A minimal faithful permutation representation — 2 generators on 46 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(38,39)(40,41,42,43,44);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(20,21,23,25,27,29,31,33,35,36,34,32,30,28,26,24,22)(37,38,39)(45,46)

Conjugacy classes & character table

4860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 118);