Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33531 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3584 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
1090 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)(14,15,20,25)(16,26,29,55)(17,22,31,46)(18,34,39,69)(19,40,37,24)(21,42,44,28)(23,49,52,38)(27,56,57,54)(30,61,41,50)(32,63,36,68)(33,66,62,48)(35,53,71,45)(43,60,73,58)(47,72,51,65)(59,77,67,75)(64,76,70,74);(14,16)(15,21)(17,27)(18,35)(19,41)(20,29)(22,43)(23,50)(24,53)(25,44)(26,34)(28,38)(30,37)(31,57)(32,64)(33,67)(36,70)(39,71)(40,45)(42,49)(46,73)(47,75)(48,76)(51,77)(52,61)(54,68)(55,69)(56,63)(58,65)(59,62)(60,72)(66,74);(14,17)(15,22)(16,27)(18,36)(19,33)(20,31)(21,43)(23,51)(24,48)(25,46)(26,54)(28,60)(29,57)(30,59)(32,39)(34,68)(35,70)(37,62)(38,72)(40,66)(41,67)(42,58)(44,73)(45,74)(47,52)(49,65)(50,77)(53,76)(55,56)(61,75)(63,69)(64,71);(17,31)(22,46)(27,57)(32,36)(33,62)(43,73)(47,51)(48,66)(54,56)(58,60)(59,67)(63,68)(64,70)(65,72)(74,76)(75,77)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26520);