Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36732 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C25×C13 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
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)(24,28)(25,29)(30,31,35,36)(32,39,42,37)(33,43,38,34)(40,41,44,45);(15,18)(19,21)(22,23,26,27)(24,29,28,25)(31,36)(33,38)(37,39)(40,44);(14,15)(16,19)(17,18)(20,21)(22,24)(23,25)(26,28)(27,29)(30,32,35,42)(31,37,36,39)(33,40,38,44)(34,41,43,45);(14,15)(16,19)(17,18)(20,21)(22,23)(24,25)(26,27)(28,29)(30,33,35,38)(31,34,36,43)(32,40,42,44)(37,41,39,45);(14,16)(15,19)(17,20)(18,21)(22,25)(23,24)(26,29)(27,28)(30,34)(31,38)(32,41)(33,36)(35,43)(37,44)(39,40)(42,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29720);