Finite Group Databasebeta

← Prev (#14301428) Next (#14301430) →

C5×#70343 #14301429

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#70343

Splittings

FittingC3×C5×#419 ⋊ C2
HallC3×C5 ⋊ #1885
SylowC3 ⋊ C5×#1885

Subgroups

subgroupG/H
centerC22×C5#937
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#419C2
socleC22×C3×C5#120
prime radicalC22×C5×D12C22
cosocleC22×C3×C4C23×C5
hypercenterC5×#419D3
hypocenterC3C5×#1885
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#419

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3,4,5)(7,8)(14,20)(16,17)(19,27)(24,26);(6,7,8)(9,11,12,10)(13,15)(14,19)(16,26)(17,24)(18,25)(20,27)(21,28)(22,23);(9,10,12,11)(13,14,17,22,18,20,16,21)(15,23,26,19,25,28,24,27)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 27127);