Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#20484 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | C23 |
| commutator | C22 | C22×C42×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C23×C13 | C23×C4 |
| prime radical | C22×D4×C13 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ G | |
1194 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(22,23,25,29,26,27,32,34)(24,28,30,35,31,33,36,37);(15,17)(18,19,21,20);(18,20,21,19)(23,27)(28,33)(29,34)(35,37);(22,24,25,30,26,31,32,36)(23,28,29,35,27,33,34,37)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13472);