Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61291 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3506 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
1810 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)(14,15,18,17)(16,20,21,19)(22,23)(24,30)(25,34)(26,28)(27,32)(29,36)(31,35)(33,37);(14,16)(15,19)(17,20)(18,21)(22,23)(24,31)(25,29)(26,28)(27,33)(30,35)(32,37)(34,36);(14,17,18,15)(16,20,21,19)(22,24)(23,27)(25,35)(26,33)(28,31)(29,37)(30,34)(32,36);(16,21)(19,20)(22,23)(24,27)(25,29)(26,28)(30,32)(31,33)(34,36)(35,37);(23,28)(27,31)(29,34)(30,37)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54279);