Finite Group Databasebeta

← Prev (#10635204) Next (#10635206) →

C3×#16598 #10635205

order768
nilpotency class2
isoclinismisoclinic class of #16249
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C24

Aliases

direct productC3×#16598

Subgroups

subgroupG/H
center, socle, prime radicalC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

1138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 768

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 9586);