Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33459 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#508 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19)(20,26)(21,29)(22,36)(23,27)(24,30)(25,32)(28,38)(31,45)(33,44)(34,42)(35,47)(37,43)(39,46)(40,49)(41,48);(18,20)(19,25)(21,31)(22,37)(23,34)(24,33)(26,36)(27,40)(28,42)(29,43)(30,41)(32,38)(35,48)(39,49)(44,46)(45,47);(14,16,17,15)(18,20)(19,26)(21,34)(22,32)(23,31)(24,33)(25,36)(27,45)(28,43)(29,42)(30,44)(35,49)(37,38)(39,48)(40,47)(41,46);(18,21,24,23)(19,27,30,29)(20,31,33,34)(22,35,39,38)(25,40,41,43)(26,42,44,45)(28,46,47,36)(32,37,48,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26447);