Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32950 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#32952 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#585 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1266 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)(16,28,33,44)(17,34,37,50)(18,24,39,49)(19,26,20,25)(22,32,45,31)(23,40,47,36)(29,54,57,42)(30,53,59,70)(35,63,66,62)(38,51,41,48)(43,61,68,58)(46,64,71,65)(52,60,69,56)(55,67,76,73)(72,74,77,75);(14,16,20,32,21,33,19,31)(15,22,26,44,27,45,25,28)(17,29,40,60,37,57,36,56)(18,30,41,61,39,59,38,58)(23,42,50,69,47,54,34,52)(24,43,51,70,49,68,48,53)(35,55,65,75,66,76,64,74)(46,67,63,77,71,73,62,72);(14,17)(15,23)(16,29)(18,35)(19,36)(20,40)(21,37)(22,42)(24,46)(25,34)(26,50)(27,47)(28,52)(30,55)(31,56)(32,60)(33,57)(38,64)(39,66)(41,65)(43,67)(44,69)(45,54)(48,62)(49,71)(51,63)(53,72)(58,74)(59,76)(61,75)(68,73)(70,77);(14,18)(15,24)(16,30)(17,35)(19,38)(20,41)(21,39)(22,43)(23,46)(25,48)(26,51)(27,49)(28,53)(29,55)(31,58)(32,61)(33,59)(34,62)(36,64)(37,66)(40,65)(42,67)(44,70)(45,68)(47,71)(50,63)(52,72)(54,73)(56,74)(57,76)(60,75)(69,77)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25940);