Finite Group Databasebeta

← Prev (#14439287) Next (#14439289) →

C5×#78531 #14439288

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

Aliases

direct productC5×#78531

Splittings

FittingC3×C4×C5×M16 ⋊ C2
HallC3×C5 ⋊ #3153
SylowC3 ⋊ C5×#3153

Subgroups

subgroupG/H
centerC22×C5C22×D12
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C4×C5×M16C2
socleC22×C3×C5C22×D4
hypercenterC4×C5×M16D3
hypocenterC3C5×#3153
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C4×C5×M16

1144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

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

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

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, 164986);