Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13323 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13324 |
| 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 | |
514 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)(14,15,21,27)(16,28,33,61)(17,34,38,58)(18,39,44,56)(19,26,20,25)(22,46,50,30)(23,45,53,37)(24,42,57,43)(29,62,65,77)(31,60,32,54)(35,69,64,59)(36,55,41,52)(40,49,67,48)(47,73,76,70)(51,66,75,63)(68,74,72,71);(14,16)(15,22)(17,35)(18,40)(19,31)(20,32)(21,33)(23,51)(24,54)(25,48)(26,49)(27,50)(28,39)(29,37)(30,43)(34,47)(36,66)(38,64)(41,63)(42,46)(44,67)(45,65)(52,59)(53,75)(55,69)(56,61)(57,60)(58,76)(62,68)(70,71)(72,77)(73,74);(14,17)(15,23)(16,29)(18,41)(19,45)(20,37)(21,38)(22,47)(24,55)(25,58)(26,34)(27,53)(28,59)(30,66)(31,35)(32,64)(33,65)(36,44)(39,72)(40,73)(42,71)(43,74)(46,63)(48,51)(49,75)(50,76)(52,57)(54,77)(56,68)(60,62)(61,69)(67,70)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6312);