Finite Group Databasebeta

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C5×#76889 #14331610

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#76889

Splittings

FittingC3×C5×#394 ⋊ C2
HallC3×C5 ⋊ #2388
SylowC3 ⋊ C5×#2388

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutator, cosocleC23×C3C24×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#394C2
socleC23×C3×C5C24
hypercenterC5×#394D3
hypocenterC3C5×#2388
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#394

1888 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)(17,19,20,23)(18,22,21,24);(7,8)(10,12)(14,16);(13,14)(15,16)(18,21)(22,24);(9,10)(11,12)(17,18)(19,22)(20,21)(23,24)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 57308);