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C5×#85856 #14479118

order1920
automorphism?
homologyAbelianization (H1) = C24×C4×C5 · Schur multiplier (H2) = C29

Aliases

direct productC5×#85856

Splittings

FittingC3×C5×#518 ⋊ C2
HallC3×C5 ⋊ #3428
SylowC3 ⋊ C5×#3428

Subgroups

subgroupG/H
centerC22×C5C24×D3
commutatorC2×C3C24×C4×C5
FrattiniC22C24×C5×D3
FittingC3×C5×#518C2
socleC22×C3×C5C25
prime radicalC22×C5×#237C2
cosocleC22×C3C25×C5
hypercenterC5×#518D3
hypocenterC3C5×#3428
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#518

3080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 5 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204816);