Finite Group Databasebeta

← Prev (#14275688) Next (#14275690) →

C3×C5×#2655 #14275689

order1920
nilpotency class2
isoclinismisoclinic class of #2613
automorphism?
homologyAbelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C23

Aliases

direct productC3×C5×#2655

Subgroups

subgroupG/H
center, socle, prime radicalC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 1387);