Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24423 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1284 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)(14,15,21,43,20,25,19,26)(16,27,41,46,31,22,30,52)(17,32,42,23,35,53,36,49)(18,37,39,50,40,24,38,51)(28,56,62,54,58,47,33,44)(29,45,60,71,61,55,59,70)(34,63,67,68,65,73,66,48)(57,75,64,69,76,72,77,74);(14,16,20,31)(15,22,25,27)(17,33,35,62)(18,29,40,61)(19,41,21,30)(23,47,49,56)(24,45,37,55)(26,52,43,46)(28,42,58,36)(32,44,53,54)(34,64,65,77)(38,60,39,59)(48,72,68,75)(50,71,51,70)(57,66,76,67)(63,69,73,74);(14,17)(15,23)(16,28)(18,34)(19,42)(20,35)(21,36)(22,44)(24,48)(25,49)(26,53)(27,54)(29,57)(30,62)(31,58)(32,43)(33,41)(37,68)(38,67)(39,66)(40,65)(45,69)(46,56)(47,52)(50,63)(51,73)(55,74)(59,64)(60,77)(61,76)(70,72)(71,75);(14,18)(15,24)(16,29)(17,34)(19,39)(20,40)(21,38)(22,45)(23,48)(25,37)(26,51)(27,55)(28,57)(30,60)(31,61)(32,63)(33,64)(35,65)(36,67)(41,59)(42,66)(43,50)(44,69)(46,71)(47,72)(49,68)(52,70)(53,73)(54,74)(56,75)(58,76)(62,77)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17411);