Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36866 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C24×C13 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(16,20)(19,21)(23,26)(27,29)(30,31,35,38)(32,36,40,34)(33,41,43,37)(39,42,45,44);(15,18)(19,21)(30,32,35,40)(31,34,38,36)(33,39,43,45)(37,42,41,44);(14,15)(16,19)(17,18)(20,21)(22,23)(24,27)(25,26)(28,29)(30,32)(31,36)(33,39)(34,38)(35,40)(37,44)(41,42)(43,45);(14,15)(16,19)(17,18)(20,21)(30,33,35,43)(31,37,38,41)(32,39,40,45)(34,42,36,44);(14,16)(15,19)(17,20)(18,21)(22,24,25,28)(23,27,26,29)(30,34,35,36)(31,32,38,40)(33,42,43,44)(37,39,41,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29854);