Finite Group Databasebeta

← Prev (#14511484) Next (#14511486) →

C5×#87551 #14511485

order1920
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C28

Aliases

direct productC5×#87551

Splittings

Fitting, HallC5×2−1+6 ⋊ C3
derived, Sylow2−1+6 ⋊ C3×C5

Subgroups

subgroupG/H
center, socle, hypercenterC2×C5C22⋊(C22⋊A4)
commutator, cosocle, hypocenter2−1+6C3×C5
FrattiniC2C5×C22⋊(C22⋊A4)
FittingC5×2−1+6C3
LCSG ▷ 2−1+6
UCSC1 ◁ C2×C5

2112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 160

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2,3,4,5)(7,12,8)(9,10,21)(13,24,33)(14,28,16)(15,25,18)(17,29,23)(19,20,22)(26,36,34)(27,37,31)(30,35,32);(7,15)(8,18)(13,27)(14,30)(16,32)(17,34)(26,29)(31,33);(6,19,11,21)(7,26,15,29)(8,31,18,33)(9,22,20,10)(12,35,25,28)(13,30,27,14)(16,34,32,17)(23,37,36,24);(6,12)(7,8)(9,23)(10,24)(11,25)(13,16)(14,17)(15,18)(19,35)(20,36)(21,28)(22,37)(26,31)(27,32)(29,33)(30,34)

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237183);