Finite Group Databasebeta

← Prev (#14302775) Next (#14302777) →

C5×#70046 #14302776

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#70046

Splittings

HallC3×C5 ⋊ #1909
SylowC3 ⋊ C5×#1909

Subgroups

subgroupG/H
centerC2×C5#4958
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#410C2
socleC2×C3×C5#386
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4C23×C5
hypercenterC5×#410D3
hypocenterC3C5×#1909
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#410

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5)(6,7,8)(9,12)(10,16)(11,20)(13,27)(14,25)(15,29)(17,32)(18,23)(19,33)(21,37)(22,36)(24,28)(26,31)(30,39)(34,40)(35,38);(7,8)(9,11,13,21,14,22,28,38)(10,15,17,19,18,30,26,34)(12,20,27,37,25,36,24,35)(16,29,32,33,23,39,31,40);(9,10)(11,19)(12,23,25,16)(13,26)(14,18)(15,21)(17,28)(20,33,36,40)(22,34)(24,31,27,32)(29,35,39,37)(30,38)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 28474);