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C5×#71324 #14317245

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

Aliases

direct productC5×#71324

Splittings

HallC3×C5 ⋊ #2211
SylowC3 ⋊ C5×#2211

Subgroups

subgroupG/H
centerC22×C5C2×#213
commutator, cosocleC2×C3×C8C23×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×#495C2
socleC22×C3×C5C2×D8
prime radicalC2×C3×C5×D8C22
hypercenterC5×#495D3
hypocenterC3C5×#2211
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C4×C5×C8 ◁ C5×#495

316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 44 points:

(1,2,3,4,5)(7,8)(13,15,16,24)(14,20,19,34)(17,30,27,44)(18,33,28,26)(21,37,35,43)(22,38,32,36)(23,40,39,29)(25,42,41,31);(6,7,8)(9,10,11,12)(14,19)(20,34)(21,35)(22,32)(23,39)(29,40)(36,38)(37,43);(10,12)(13,14)(15,23)(16,19)(17,29)(18,32)(20,25)(21,31)(22,28)(24,39)(26,43)(27,40)(30,38)(33,37)(34,41)(35,42)(36,44)

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, 42943);