Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62595 |
| 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 ◁ C4×C13×#41 ◁ G | |
1966 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)(14,15,19,21)(16,20,18,17)(22,23)(24,31)(25,29)(26,35)(27,30)(28,33)(32,37)(34,36);(14,16,19,18)(15,20,21,17)(22,24)(23,28)(25,32)(26,34)(27,33)(29,36)(30,31)(35,37);(14,17,18,15,19,20,16,21)(22,25,27,26)(23,29,30,35)(24,32,33,34)(28,36,31,37);(14,16,19,18)(15,20,21,17)(24,33)(28,31)(32,34)(36,37);(14,16,19,18)(15,20,21,17)(22,26,27,25)(23,29,30,35)(24,34,33,32)(28,36,31,37)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55583);