Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13404 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
386 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,25)(16,26,31,47)(17,32,36,69)(18,37,40,23)(19,41,44,68)(21,30,48,28)(22,49,52,35)(24,54,57,39)(27,60,33,70)(29,46,42,55)(34,72,38,56)(43,53,73,51)(45,74,50,65)(58,71,75,62)(59,64,76,66)(61,77,63,67);(14,16)(15,21)(17,33)(18,30)(19,42)(20,31)(22,50)(23,47)(24,55)(25,48)(26,37)(27,36)(28,40)(29,44)(32,67)(34,61)(35,62)(38,63)(39,64)(41,59)(43,65)(45,52)(46,57)(49,71)(51,75)(53,58)(54,66)(56,60)(68,76)(69,77)(70,72)(73,74);(14,17,20,36)(15,22,25,52)(16,27)(18,38,40,34)(19,43,44,73)(21,45)(23,53,37,51)(24,56,57,72)(26,58)(28,63)(29,65)(30,61)(31,33)(32,68,69,41)(35,54,49,39)(42,74)(46,60)(47,75)(48,50)(55,70)(59,77)(62,66)(64,71)(67,76)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6393);