Finite Group Databasebeta

← Prev (#14324379) Next (#14324381) →

C5×#83172 #14324380

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25×C4

Aliases

direct productC5×#83172

Splittings

HallC3×C5 ⋊ #2328
SylowC3 ⋊ C5×#2328

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
Fitting, prime radicalC2×C3×C5×#127C2
socleC23×C3×C5C24
cosocleC23×C3C24×C5
hypercenterC2×C5×#127D3
hypocenterC3C5×#2328
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×#127

1480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 50078);