Finite Group Databasebeta

← Prev (#14511009) Next (#14511011) →

C5×#73286 #14511010

order1920
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C22×C4

Aliases

direct productC5×#73286

Splittings

Fitting, HallC5×#2276 ⋊ C3
derived, Sylow#2276 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5C22⋊(C42⋊C3)
commutator, cosocle, hypocenter#2276C3×C5
FrattiniC23C5×C22⋊A4
FittingC5×#2276C3
socleC23×C5C22⋊A4
LCSG ▷ #2276
UCSC1 ◁ C2×C5

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 25 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236708);