Finite Group Databasebeta

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C5×#86150 #14484111

order1920
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C28

Aliases

direct productC5×#86150

Splittings

FittingC3×C5×#529 ⋊ C2
HallC3×C5 ⋊ #3475
SylowC3 ⋊ C5×#3475

Subgroups

subgroupG/H
centerC2×C4×C5C23×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC3×C5×#529C2
socleC22×C3×C5C25
hypercenterC5×#529D3
hypocenterC3C5×#3475
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C5×#529

2264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 5 generators on 24 points:

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

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, 209809);