Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13062 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×D8 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C24×C13 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
506 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
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)(23,27)(24,31)(25,32)(28,33)(29,34)(30,37)(35,36);(19,21)(22,23,28,37,25,30,24,27,26,29,31,36,32,35,33,34);(15,17)(23,29)(27,34)(30,35)(36,37)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6050);