Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13308 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3061 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
532 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)(18,19,24,30)(20,31,34,47)(21,35,39,46)(22,29,23,28)(25,41,44,32)(26,40,45,33)(27,37,42,38)(36,48,49,43);(14,15)(16,17)(18,20)(19,25)(21,36)(22,33)(23,40)(24,34)(26,42)(27,45)(28,43)(29,48)(30,44)(31,35)(32,38)(37,41)(39,49)(46,47);(15,17)(18,20)(19,26)(21,32)(22,40)(23,33)(24,34)(25,42)(27,44)(28,47)(29,31)(30,45)(35,48)(36,38)(37,49)(39,41)(43,46)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6296);