Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24987 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#24989 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
620 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)(14,15,21,27)(16,28,33,46)(17,34,38,53)(18,39,42,51)(19,26,20,25)(22,32,47,31)(23,43,50,37)(24,41,52,40)(29,48,35,44)(30,58,61,45)(36,66,68,49)(54,62,63,57)(55,60,71,59)(56,75,65,74)(64,69,73,67)(70,76,72,77);(14,16,20,32,21,33,19,31)(15,22,26,46,27,47,25,28)(17,35,37,62,38,29,43,57)(18,30,41,60,42,61,40,59)(23,48,34,63,50,44,53,54)(24,45,51,71,52,58,39,55)(36,65,67,77,68,56,69,76)(49,72,64,75,66,70,73,74);(14,17)(15,23)(16,29)(18,36)(19,37)(20,43)(21,38)(22,44)(24,49)(25,34)(26,53)(27,50)(28,54)(30,56)(31,57)(32,62)(33,35)(39,64)(40,67)(41,69)(42,68)(45,70)(46,63)(47,48)(51,73)(52,66)(55,74)(58,72)(59,76)(60,77)(61,65)(71,75);(14,18,20,41,21,42,19,40)(15,24,26,51,27,52,25,39)(16,30,32,60,33,61,31,59)(17,36,43,69,38,68,37,67)(22,45,46,71,47,58,28,55)(23,49,53,73,50,66,34,64)(29,56,62,77,35,65,57,76)(44,70,63,75,48,72,54,74)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17977);