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C5×#80042 #14424795

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#80042

Splittings

FittingC3×C5×#448 ⋊ C2
HallC3×C5 ⋊ #3013
SylowC3 ⋊ C5×#3013

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#448C2
socleC22×C3×C5C22×D4
hypercenterC5×#448D3
hypocenterC3C5×#3013
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#448

1424 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)(13,15,17,21)(14,19,20,26)(16,22,23,27)(18,25,24,28);(6,7,8)(10,12)(15,21)(19,26)(22,27)(25,28);(13,14,17,20)(15,19,21,26)(16,24,23,18)(22,28,27,25);(9,10)(11,12)(14,18)(16,23)(19,25)(20,24)(22,27)(26,28)

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, 150493);