Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13402 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13403 |
| 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 | |
384 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)(16,26,31,46)(17,32,37,67)(18,38,40,23)(19,41,43,65)(21,30,47,28)(22,48,52,35)(24,53,55,39)(27,57,60,77)(29,45,64,75)(33,68,58,76)(34,66,36,54)(42,51,69,50)(44,72,74,62)(49,71,73,59)(56,61,70,63);(14,16)(15,21)(17,33)(18,30)(19,29)(20,31)(22,49)(23,46)(24,45)(25,47)(26,38)(27,36)(28,40)(32,57)(34,60)(35,62)(37,58)(39,63)(41,70)(42,71)(43,64)(44,51)(48,72)(50,74)(52,73)(53,61)(54,76)(55,75)(56,65)(59,69)(66,68)(67,77);(14,17,20,37)(15,22,25,52)(16,27)(18,36,40,34)(19,42,43,69)(21,44)(23,51,38,50)(24,54,55,66)(26,49)(28,33)(29,62)(30,58)(31,60)(32,65,67,41)(35,53,48,39)(45,57)(46,73)(47,74)(56,76)(59,63)(61,71)(64,72)(68,70)(75,77)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6391);