Finite Group Databasebeta

← Prev (#14284582) Next (#14284584) →

C5×#70431 #14284583

order1920
isoclinismisoclinic class of #4451
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#70431

Splittings

FittingC2×C3×C5×C4⋊C8 ⋊ C2
HallC3×C5 ⋊ #1540
SylowC3 ⋊ C5×#1540

Subgroups

subgroupG/H
centerC2×C4×C5(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC2×C3×C5×C4⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5477C2
cosocleC3×C42C23×C5
hypercenterC2×C5×C4⋊C8D3
hypocenterC3C5×#1540
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ C2×C5×C4⋊C8

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 10281);