Finite Group Databasebeta

← Prev (#14277013) Next (#14277015) →

C5×#67752 #14277014

order1920
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#67752

Splittings

HallC3×C5 ⋊ #1288
SylowC3 ⋊ C5×#1288

Subgroups

subgroupG/H
centerC22×C5C3⋊#95
commutatorC2×C3×C4C42×C5
FrattiniC2×C42C2×C5×D3
FittingC3×C5×#432C2
socleC22×C3×C5#95
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C3×C42C22×C5
hypercenterC5×#432D3
hypocenterC3C5×#1288
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C5×#432

304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2712);