Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13392 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #482 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #2033 |
| prime radical | C13×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
386 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)(16,26)(17,32)(18,38)(19,41)(20,25)(21,28)(22,35)(23,40)(24,39)(27,57)(29,46)(30,47)(31,48)(33,67)(34,65)(36,66)(37,53)(42,52)(43,50)(44,71)(45,73)(49,70)(51,69)(54,72)(55,59)(56,62)(58,74)(60,76)(61,75)(63,64)(68,77);(14,16)(15,21)(17,33)(18,30)(19,42)(20,31)(22,45)(23,48)(24,52)(25,47)(26,38)(27,36)(28,40)(29,44)(32,64)(34,58)(35,59)(37,63)(39,60)(41,56)(43,61)(46,54)(49,77)(50,55)(51,75)(53,57)(62,72)(65,67)(66,74)(68,69)(70,73)(71,76);(14,17,18,34,20,36,40,37)(15,22,23,49,25,51,38,50)(16,27,28,58,31,33,30,63)(19,43,39,69,44,70,72,35)(21,45,26,55,47,75,48,77)(24,53,41,66,54,65,71,32)(29,61,60,59,42,73,62,68)(46,67,56,74,52,57,76,64)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6380);