Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#10992 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | #120 |
| commutator | C24 | C22×C4×C13 |
| Frattini, cosocle | C25 | C23×C13 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C25×C13 ◁ G | |
1658 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,30,32,27)(25,28)(26,29)(31,34,37,35)(33,36);(15,17)(22,24)(23,27)(25,31)(26,32)(28,35)(29,30)(33,37)(34,36);(19,21)(22,25,26,33)(23,28,29,36)(24,31,32,37)(27,34,30,35)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3980);