Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13314 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
536 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)(18,19,24,30)(20,31,35,44)(21,25,38,41)(22,29,23,28)(26,32,45,34)(27,37,40,36)(33,43,48,42)(39,47,46,49);(19,25)(20,32)(21,36)(22,23)(26,42)(27,28)(29,40)(30,41)(31,46)(33,48)(34,35)(37,38)(39,44)(43,45);(15,17)(18,20)(19,26)(21,33)(22,32)(23,34)(24,35)(25,39)(27,43)(28,44)(29,31)(30,45)(36,47)(37,49)(38,48)(40,42)(41,46)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6302);