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×#13401 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #482 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #2034 |
| prime radical | C13×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
390 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)(18,37)(19,41)(20,25)(21,28)(22,35)(23,40)(24,39)(27,55)(29,45)(30,46)(31,47)(33,66)(34,68)(36,65)(38,51)(42,50)(43,64)(44,60)(48,71)(49,70)(52,69)(53,57)(54,61)(56,77)(58,63)(59,72)(62,76)(67,74)(73,75);(14,16)(15,21)(17,33)(18,30)(19,29)(20,31)(22,44)(23,47)(24,45)(25,46)(26,37)(27,36)(28,40)(32,63)(34,56)(35,67)(38,58)(39,61)(41,72)(42,73)(43,62)(48,53)(49,75)(50,74)(51,55)(52,76)(54,64)(57,70)(59,69)(60,71)(65,77)(66,68);(14,17,20,36)(15,22,25,49)(16,27)(18,38,40,34)(19,42,43,71)(21,44)(23,50,37,48)(24,51,52,68)(26,53)(28,58)(29,60)(30,56)(31,33)(32,64,65,41)(35,69,70,39)(45,55)(46,75)(47,74)(54,77)(57,61)(59,67)(62,73)(63,72)(66,76)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6389);