Finite Group Databasebeta

← Prev (#14275258) Next (#14275260) →

C3×C5×#2225 #14275259

order1920
nilpotency class4
isoclinismisoclinic class of #2184
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C5×#2225

Subgroups

subgroupG/H
center, socle, prime radicalC22×C3×C5C2×D8
commutator, Frattini, cosocleC2×C8C23×C3×C5
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ C3×C4×C5×C8 ◁ G

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

435 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 957);