Finite Group Databasebeta

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C5×#73447 #14324438

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

Aliases

direct productC5×#73447

Splittings

HallC3×C5 ⋊ #2329
SylowC3 ⋊ C5×#2329

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC4×C5×C22⋊C4D3
hypocenterC3C5×#2329
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C4×C5×C22⋊C4

1056 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 50136);