Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#7168 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #95 |
| commutator | C2×C4 | C4×C8×C13 |
| Frattini, cosocle | C2×C4×C8 | C22×C13 |
| socle | C22×C13 | #336 |
| prime radical | C23×C13 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C4×C8×C13 ◁ G | |
254 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19)(16,17)(20,21)(22,23,26,30,27,31,36,33,28,32,37,24,25,29,35,34);(14,15,17,20,18,21,16,19)(22,24,26,31,27,34,36,32,28,30,37,29,25,33,35,23)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 156);