Finite Group Databasebeta

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C5×#80627 #14453688

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#80627

Splittings

FittingC3×C5×#464 ⋊ C2
HallC3×C5 ⋊ #3266
SylowC3 ⋊ C5×#3266

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#464C2
socleC22×C3×C5C22×D4
prime radicalC5×#5676C2
hypercenterC5×#464D3
hypocenterC3C5×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#464

988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 179386);