Finite Group Databasebeta

← Prev (#14331350) Next (#14331352) →

C5×#75494 #14331351

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#75494

Splittings

HallC3×C5 ⋊ #2383
SylowC3 ⋊ C5×#2383

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC5×#388D3
hypocenterC3C5×#2383
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#388

912 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 57049);