Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13417 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13418 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2041 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
422 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)(16,30)(17,37)(18,28)(19,44)(20,26)(21,25)(22,29)(23,32)(24,40)(27,46)(31,63)(33,50)(34,51)(35,53)(36,52)(38,49)(39,56)(41,61)(42,74)(43,58)(45,55)(47,57)(48,73)(54,66)(59,67)(60,69)(62,65)(64,75)(68,76)(70,72)(71,77);(14,16,22,36)(15,23,29,53)(17,38,42,68)(18,35,21,32)(19,34,46,67)(20,33,43,69)(24,54,57,63)(25,52,28,30)(26,59,58,51)(27,60,44,50)(31,45,66,41)(37,72,74,62)(39,65,48,70)(40,64,47,71)(49,73,76,56)(55,77,61,75);(14,17,18,39,22,42,21,48)(15,24,25,55,29,57,28,61)(16,31,32,64,36,66,35,71)(19,45,43,40,46,41,20,47)(23,49,30,62,53,76,52,72)(26,56,27,37,58,73,44,74)(33,68,67,65,69,38,34,70)(50,54,51,75,60,63,59,77)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6406);