Finite Group Databasebeta

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C5×#68960 #14298629

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#68960

Splittings

FittingC3×C5×#342 ⋊ C2
HallC3×C5 ⋊ #1828
SylowC3 ⋊ C5×#1828

Subgroups

subgroupG/H
centerC2×C5#4664
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC3×C5×#342C2
socleC2×C3×C5#381
prime radicalC22×C5×#67C22
cosocleC24×C3C23×C5
hypercenterC5×#342D3
hypocenterC3C5×#1828
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C24×C5 ◁ C5×#342

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

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

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, 24327);