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C5×#81891 #14439831

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#81891

Splittings

FittingC3×C5×#498 ⋊ C2
HallC3×C5 ⋊ #3160
SylowC3 ⋊ C5×#3160

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#498C2
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenterC5×#498D3
hypocenterC3C5×#3160
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#498

712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 165529);