Finite Group Databasebeta

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C5×#79917 #14418460

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#79917

Splittings

FittingC3×C5×C8×Q8 ⋊ C2
HallC3×C5 ⋊ #2960
SylowC3 ⋊ C5×#2960

Subgroups

subgroupG/H
centerC2×C5×C8C22×D3
commutatorC22×C3C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×C8×Q8C2
socleC22×C3×C5C23×C4
prime radicalC22×C5×D3C22×C4
cosocleC2×C3×C4C24×C5
hypercenterC5×C8×Q8D3
hypocenterC3C5×#2960
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C5×C8 ◁ C5×C8×Q8

728 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)(7,8)(18,23)(22,28)(24,30)(29,32);(6,7,8)(17,19,20,25,21,26,27,31)(18,22,24,29,23,28,30,32);(9,11,12,16)(10,13,14,15);(9,10,12,14)(11,15,16,13)(17,18,20,24,21,23,27,30)(19,22,25,29,26,28,31,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 144158);