Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13×C16 · Schur multiplier (H2) = C22 |
| direct product | C13×#13645 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C13×C16 | C23 |
| commutator | C22 | C22×C13×C16 |
| Frattini, cosocle | C2×C16 | C23×C13 |
| socle | C22×C13 | C22×C16 |
| prime radical | C2×D4×C13 | C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C13×C16 ◁ G | |
204 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,21,26,22,27,33,41,23,20,29,30,35,31,44,45,24,28,34,42,36,43,47,49,37,32,25,38,39,46,40,48);(15,17);(18,20,21,30,22,31,33,45,23,28,29,42,35,43,44,49,24,32,34,38,36,46,47,48,37,19,25,26,39,27,40,41)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6633);