Finite Group Databasebeta

← Prev (#14278753) Next (#14278755) →

C5×#67813 #14278754

order1920
automorphism?
homologyAbelianization (H1) = C4×C5×C8 · Schur multiplier (H2) = C22

Aliases

direct productC5×#67813

Splittings

HallC3×C5 ⋊ #1378
SylowC3 ⋊ C5×#1378

Subgroups

subgroupG/H
centerC5×C8#217
commutatorC22×C3C4×C5×C8
FrattiniC22×C8C2×C5×D3
FittingC2×C3×C5×M32C2
socleC2×C3×C5#336
prime radicalC23×C3×C5C2×C8
cosocleC22×C3×C8C22×C5
hypercenterC2×C5×M32D3
hypocenterC3C5×#1378
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C5×C8 ◁ C22×C5×C8 ◁ C2×C5×M32

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 40 points:

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

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, 4452);