Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13310 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13311 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
520 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)(16,28)(17,34)(18,38)(19,27)(20,25)(21,26)(22,30)(23,36)(24,41)(29,58)(31,51)(32,56)(33,57)(35,67)(37,54)(39,45)(40,53)(42,52)(43,50)(44,68)(46,63)(47,62)(48,73)(49,70)(55,60)(59,65)(61,75)(64,74)(66,69)(71,76)(72,77);(14,16,21,33)(15,22,26,46)(17,29,37,61)(18,39,42,62)(19,32,20,31)(23,48,50,44)(24,51,53,56)(25,47,27,45)(28,52,57,38)(30,40,63,41)(34,65,54,72)(35,68,70,73)(36,64,43,60)(49,75,67,58)(55,66,74,76)(59,71,77,69);(14,17)(15,23)(16,29)(18,35)(19,43)(20,36)(21,37)(22,44)(24,49)(25,54)(26,50)(27,34)(28,55)(30,59)(31,64)(32,60)(33,61)(38,66)(39,68)(40,71)(41,69)(42,70)(45,72)(46,48)(47,65)(51,58)(52,76)(53,67)(56,75)(57,74)(62,73)(63,77)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6299);