Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12926 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
400 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)(14,15,17,16)(18,19,24,30)(20,32,21,35)(22,38,41,47)(23,31,25,29)(26,36,45,33)(27,34,46,37)(28,40,43,42)(39,48,49,44);(14,16,17,15)(18,20,24,21)(19,26,30,45)(22,39,41,49)(23,34,25,37)(27,43,46,28)(29,44,31,48)(32,47,35,38)(33,40,36,42);(18,21,24,20)(19,27,30,46)(22,36,41,33)(23,34,25,37)(26,43,45,28)(29,32,31,35)(38,44,47,48)(39,42,49,40)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5914);