Finite Group Databasebeta

← Prev (#14326165) Next (#14326167) →

C5×#82457 #14326166

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#82457

Splittings

FittingC2×C3×C4×C5×Q8 ⋊ C2
HallC3×C5 ⋊ #2341
SylowC3 ⋊ C5×#2341

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC2×C3×C4×C5×Q8C2
socleC23×C3×C5C24
prime radicalC22×C5×#239C2
cosocleC23×C3C24×C5
hypercenterC2×C4×C5×Q8D3
hypocenterC3C5×#2341
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×Q8

1744 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)(17,20,21,19)(18,23,22,24);(7,8)(14,16)(17,19,21,20)(18,23,22,24);(17,18,21,22)(19,23,20,24);(9,10,11,12)(13,14)(15,16)(18,22)(23,24)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 51864);