Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#34621 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| prime radical | C13×#2619 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
1918 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)(14,15)(16,19)(17,18)(20,21)(22,23,25,27)(24,26,28,29)(32,36)(35,37);(15,18)(19,21)(22,24,25,28)(23,26,27,29)(30,31)(32,35)(33,34)(36,37);(23,27)(26,29)(31,34)(35,37);(30,32,33,36)(31,35,34,37);(14,16,17,20)(15,19,18,21)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27609);