Finite Group Databasebeta

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C5×#81216 #14472082

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

Aliases

direct productC5×#81216

Splittings

FittingC3×C5×#479 ⋊ C2
HallC3×C5 ⋊ #3364
SylowC3 ⋊ C5×#3364

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#479C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×D12C23
hypercenterC5×#479D3
hypocenterC3C5×#3364
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#479

672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 197780);