Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12954 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1864 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
380 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)(14,15,19,24,20,26,44,25)(16,27,31,59,32,47,42,54)(17,33,35,55,36,71,43,70)(18,37,40,23,41,56,65,57)(21,45,48,29,50,38,49,30)(22,39,51,34,53,72,52,73)(28,60,63,77,64,46,68,76)(58,67,75,62,69,66,74,61);(14,16,20,32)(15,21)(17,28,36,64)(18,38,41,45)(19,42,44,31)(22,46)(23,54)(24,49)(25,48)(26,50)(27,37)(29,65,30,40)(33,69)(34,67,73,66)(35,68,43,63)(39,62,72,61)(47,56)(51,77)(52,76)(53,60)(55,75)(57,59)(58,71)(70,74);(14,17,20,36)(15,22,26,53)(16,28,32,64)(18,39,41,72)(19,43,44,35)(21,46,50,60)(23,55,57,70)(24,52,25,51)(27,58,47,69)(29,66,30,67)(31,68,42,63)(33,37,71,56)(34,40,73,65)(38,62,45,61)(48,77,49,76)(54,75,59,74)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5942);