Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13406 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #469 |
| 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)(16,27)(17,33)(18,25)(19,41)(20,26)(21,29)(22,36)(23,40)(24,39)(28,59)(30,46)(31,48)(32,47)(34,67)(35,68)(37,54)(38,66)(42,53)(43,52)(44,55)(45,64)(49,75)(50,71)(51,72)(56,70)(57,61)(58,65)(60,77)(62,76)(63,74)(69,73);(14,16)(15,21)(17,34)(18,31)(19,42)(20,32)(22,49)(23,47)(24,53)(25,27)(26,48)(28,37)(29,40)(30,44)(33,59)(35,62)(36,69)(38,60)(39,63)(41,58)(43,61)(45,50)(46,56)(51,57)(52,73)(54,77)(55,74)(64,72)(65,70)(66,76)(67,68)(71,75);(14,17,20,38)(15,22,26,51)(16,28)(18,37,40,35)(19,43,44,71)(21,45)(23,52,25,50)(24,54,56,68)(27,57)(29,34)(30,64)(31,60)(32,62)(33,55,66,41)(36,70,72,39)(42,69)(46,59)(47,49)(48,73)(53,76)(58,77)(61,65)(63,75)(67,74)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6394);