Finite Group Databasebeta

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C5×#68991 #14298400

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#68991

Splittings

FittingC3×C5×#343 ⋊ C2
HallC3×C5 ⋊ #1822
SylowC3 ⋊ C5×#1822

Subgroups

subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#343C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3C2×C4
cosocleC22×C3×C4C23×C5
hypercenterC5×#343D3
hypocenterC3C5×#1822
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#343

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 32 points:

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

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, 24098);