Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#60046 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1898 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(23,27)(24,29)(30,31,35,33)(32,34,37,36);(16,20)(19,21)(23,27)(24,29)(30,32,35,37)(31,36,33,34);(14,15,18,17)(16,19,20,21)(22,23)(24,28)(25,29)(26,27)(30,33,35,31)(32,34,37,36);(14,16,18,20)(15,19,17,21)(22,24,26,29)(23,28,27,25);(14,17,18,15)(16,21,20,19)(22,25,26,28)(23,29,27,24)(30,34)(31,32)(33,37)(35,36)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53034);