Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33441 |
| subgroup | G/H | |
|---|---|---|
| center | C13×C16 | C2×D4 |
| commutator | C4 | C23×C8×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C2×C8×D4 |
| prime radical | C13×#575 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C13×C16 ◁ C22×C13×C16 ◁ G | |
646 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)(14,15,19,26,20,25,39,50,21,24,40,49,18,36,38,62)(16,27,30,52,29,22,41,44,31,45,56,69,37,43,63,68)(17,23,33,48,34,47,60,71,35,46,61,70,32,57,59,74)(28,51,54,72,53,42,64,66,55,67,73,77,58,65,75,76);(14,16)(15,22)(17,28)(18,37)(19,30)(20,29)(21,31)(23,42)(24,43)(25,45)(26,44)(27,36)(32,58)(33,54)(34,53)(35,55)(38,63)(39,41)(40,56)(46,65)(47,67)(48,66)(49,68)(50,69)(51,57)(52,62)(59,75)(60,64)(61,73)(70,76)(71,77)(72,74);(14,17,19,33,20,34,39,60,21,35,40,61,18,32,38,59)(15,23,26,48,25,47,50,71,24,46,49,70,36,57,62,74)(16,28,30,54,29,53,41,64,31,55,56,73,37,58,63,75)(22,42,44,66,45,67,69,77,43,65,68,76,27,51,52,72);(15,24)(22,43)(23,46)(25,36)(26,49)(27,45)(42,65)(44,68)(47,57)(48,70)(50,62)(51,67)(52,69)(66,76)(71,74)(72,77)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26429);