Finite Group Databasebeta

← Prev (#14294778) Next (#14294780) →

C5×#71587 #14294779

order1920
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#71587

Splittings

HallC3×C5 ⋊ #1742
SylowC3 ⋊ C5×#1742

Subgroups

subgroupG/H
centerC2×C4×C5#217
commutatorC22×C3C2×C42×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#117C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#117D3
hypocenterC3C5×#1742
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ C2×C5×#117

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20477);