Finite Group Databasebeta

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C5×#74297 #14327489

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

Aliases

direct productC5×#74297

Splittings

FittingC3×C5×#383 ⋊ C2
HallC3×C5 ⋊ #2353
SylowC3 ⋊ C5×#2353

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#383C2
socleC23×C3×C5C24
prime radicalC22×C5×D12C22
cosocleC23×C3C24×C5
hypercenterC5×#383D3
hypocenterC3C5×#2353
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#383

1176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

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

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

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, 53187);