Finite Group Databasebeta

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C5×#73669 #14332542

order1920
isoclinismisoclinic class of #4656
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#73669

Splittings

HallC3×C5 ⋊ #2399
SylowC3 ⋊ C5×#2399

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutator, cosocleC23×C3C24×C5
FrattiniC23C23×C5×D3
FittingC3×C4×C5×C4⋊C4C2
socle, prime radicalC23×C3×C5C24
hypercenterC4×C5×C4⋊C4D3
hypocenterC3C5×#2399
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C4×C5×C4⋊C4

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 4 generators on 28 points:

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

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, 58240);