Finite Group Databasebeta

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C5×#73877 #14326163

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#73877

Splittings

FittingC3×C5×#380 ⋊ C2
HallC3×C5 ⋊ #2341
SylowC3 ⋊ C5×#2341

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#380C2
socleC23×C3×C5C24
prime radicalC22×C5×#235C2
cosocleC23×C3C24×C5
hypercenterC5×#380D3
hypocenterC3C5×#2341
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#380

1744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3,4,5)(6,7,8)(17,20,21,19)(18,23,22,24);(14,16)(17,19,21,20)(18,23,22,24);(7,8)(17,18,21,22)(19,23,20,24);(7,8)(9,10,11,12)(13,14)(15,16)(18,22)(23,24)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 51861);