Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13389 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13390 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2033 |
| 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 | |
382 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)(17,32,36,67)(18,38,40,23)(19,41,43,72)(21,30,47,28)(22,48,51,35)(24,53,55,39)(27,58,33,69)(29,45,64,76)(34,68,37,54)(42,52,71,50)(44,62,49,74)(56,70,77,60)(57,61,73,63)(59,75,65,66);(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)(32,66)(34,59)(35,70)(37,65)(39,63)(41,73)(42,74)(43,64)(44,51)(48,60)(50,56)(52,77)(53,61)(54,58)(55,76)(57,72)(62,71)(67,75)(68,69);(14,17,18,34,20,36,40,37)(15,22,23,50,25,51,38,52)(16,27,28,59,31,33,30,65)(19,42,39,48,43,71,53,35)(21,44,26,56,47,49,46,77)(24,54,41,67,55,68,72,32)(29,62,61,60,64,74,63,70)(45,69,57,75,76,58,73,66)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6378);