Finite Group Databasebeta

← Prev (#14275495) Next (#14275497) →

C3×C5×#2462 #14275496

order1920
nilpotency class2
isoclinismisoclinic class of #2403
automorphism?
homologyAbelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24

Aliases

direct productC3×C5×#2462

Subgroups

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

904 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 1920

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

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

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 1194);