Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61619 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#525 ◁ G | |
2088 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
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)(16,20)(17,19)(18,21)(23,28)(24,31)(25,27)(29,36)(32,34)(35,37);(14,16)(15,18)(17,21)(19,20)(22,23,26,28)(24,29,32,35)(25,33,27,30)(31,37,34,36);(22,24)(23,29)(25,31)(26,32)(27,34)(28,35)(30,36)(33,37);(16,21)(18,20)(23,28)(29,35)(30,33)(36,37);(15,19)(18,20)(22,25,26,27)(23,30,28,33)(24,31,32,34)(29,36,35,37)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54607);