Finite Group Databasebeta

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C5×#68127 #14281139

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

Aliases

direct productC5×#68127

Splittings

HallC3×C5 ⋊ #1467
SylowC3 ⋊ C5×#1467

Subgroups

subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#324C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4C23×C5
hypercenterC5×#324D3
hypocenterC3C5×#1467
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#324

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

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, 6837);