Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12947 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1862 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×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)(14,15,20,27,22,28,21,43)(16,29,33,59,34,60,44,47)(17,35,38,56,39,71,45,51)(18,26,40,55,41,57,19,25)(23,32,48,67,50,69,49,31)(24,36,52,73,54,42,53,37)(30,61,64,75,66,76,65,46)(58,68,74,72,77,62,70,63);(14,16,20,33,22,34,21,44)(15,23,27,48,28,50,43,49)(17,30,38,64,39,66,45,65)(18,32,40,67,41,69,19,31)(24,46,52,61,54,75,53,76)(25,47,26,29,55,59,57,60)(35,70,56,58,71,74,51,77)(36,72,73,62,42,63,37,68);(14,17)(15,24)(16,30)(18,37)(19,42)(20,38)(21,45)(22,39)(23,46)(25,35)(26,56)(27,52)(28,54)(29,58)(31,63)(32,68)(33,64)(34,66)(36,40)(41,73)(43,53)(44,65)(47,70)(48,61)(49,76)(50,75)(51,57)(55,71)(59,74)(60,77)(62,69)(67,72)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5935);