Finite Group Databasebeta

← Prev (#14285335) Next (#14285337) →

C5×#70824 #14285336

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#70824

Splittings

HallC3×C5 ⋊ #1558
SylowC3 ⋊ C5×#1558

Subgroups

subgroupG/H
centerC22×C5C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#432C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C42C23×C5
hypercenterC5×#432D3
hypocenterC3C5×#1558
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C5×#432

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

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

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, 11034);