Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24810 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,42,21,26,20,25)(16,27,30,22,32,46,31,47)(17,33,43,23,37,50,36,51)(18,38,39,24,41,66,40,52)(28,44,34,48,56,70,55,69)(29,57,58,53,60,45,59,71)(35,49,67,65,64,73,63,61)(54,72,62,76,75,77,74,68);(14,16,19,30,21,32,20,31)(15,22,25,27,26,47,42,46)(17,34,36,28,37,55,43,56)(18,29,39,58,41,60,40,59)(23,48,50,70,51,69,33,44)(24,45,38,53,52,57,66,71)(35,62,63,54,64,74,67,75)(49,72,65,76,73,77,61,68);(14,17)(15,23)(16,28)(18,35)(19,36)(20,43)(21,37)(22,44)(24,49)(25,50)(26,51)(27,48)(29,54)(30,55)(31,34)(32,56)(33,42)(38,65)(39,63)(40,67)(41,64)(45,68)(46,69)(47,70)(52,73)(53,72)(57,76)(58,74)(59,62)(60,75)(61,66)(71,77);(14,18,20,40,21,41,19,39)(15,24,42,66,26,52,25,38)(16,29,31,59,32,60,30,58)(17,35,43,67,37,64,36,63)(22,45,46,71,47,57,27,53)(23,49,33,61,51,73,50,65)(28,54,34,62,56,75,55,74)(44,68,69,77,70,76,48,72)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17798);