Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61687 |
| 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×#532 ◁ G | |
2068 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)(16,20)(17,19)(18,21)(22,23,27,26)(24,31,30,28)(25,32,34,37)(29,36,33,35);(14,16)(15,18)(17,21)(19,20)(22,24)(23,28)(25,32)(26,31)(27,30)(29,36)(33,35)(34,37);(22,25,27,34)(23,29,26,33)(24,32,30,37)(28,36,31,35);(16,21)(18,20)(22,26,27,23)(24,31,30,28)(25,33,34,29)(32,35,37,36);(15,19)(18,20)(23,26)(24,30)(29,33)(32,37)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54675);