Finite Group Databasebeta

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C5×#86274 #14481801

order1920
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C28

Aliases

direct productC5×#86274

Splittings

FittingC3×C5×#533 ⋊ C2
HallC3×C5 ⋊ #3458
SylowC3 ⋊ C5×#3458

Subgroups

subgroupG/H
centerC2×C4×C5C23×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC3×C5×#533C2
socleC22×C3×C5C25
prime radicalC23×C5×D3C23
hypercenterC5×#533D3
hypocenterC3C5×#3458
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C5×#533

1992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 5 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 207499);