Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13332 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G | |
566 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
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)(20,30)(21,26)(22,28)(23,39)(24,29)(25,32)(27,36)(31,40)(33,45)(34,47)(35,46)(37,43)(38,44)(41,49)(42,48);(15,17)(18,20,24,34)(19,25,29,42)(21,35,38,49)(22,31,23,33)(26,30,44,47)(27,45,43,40)(28,46,39,41)(32,37,48,36);(19,26)(20,31)(21,36)(22,23)(25,40)(27,28)(29,44)(30,46)(32,48)(33,34)(37,38)(39,43)(41,47)(42,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6320);