Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C22×#102 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#578 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
1102 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)(14,15,19,24,20,26,40,25)(16,27,30,49,31,54,39,53)(17,22,34,47,32,45,61,48)(18,35,37,23,38,50,66,51)(21,36,42,29,44,58,43,59)(28,52,57,71,55,73,65,74)(33,62,64,46,60,72,77,70)(41,63,68,56,67,76,69,75);(14,16,20,31)(15,21,26,44)(17,28,32,55)(18,36,38,58)(19,39,40,30)(22,41,45,67)(23,49,51,53)(24,43,25,42)(27,35,54,50)(29,37,59,66)(33,63,60,76)(34,65,61,57)(46,71,70,74)(47,69,48,68)(52,62,73,72)(56,64,75,77);(14,17)(15,22)(16,28)(18,33)(19,34)(20,32)(21,41)(23,46)(24,47)(25,48)(26,45)(27,52)(29,56)(30,57)(31,55)(35,62)(36,63)(37,64)(38,60)(39,65)(40,61)(42,68)(43,69)(44,67)(49,71)(50,72)(51,70)(53,74)(54,73)(58,76)(59,75)(66,77);(17,32)(22,45)(28,55)(33,60)(34,61)(41,67)(46,70)(47,48)(52,73)(56,75)(57,65)(62,72)(63,76)(64,77)(68,69)(71,74)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26381);