Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13215 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13216 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1961 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
434 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)(17,33,37,66)(18,39)(19,25)(20,43)(21,26)(22,30)(23,36,51,38)(24,40)(28,52)(29,59,61,75)(31,54)(32,56)(34,67,70,53)(35,71,72,50)(41,44)(42,55)(45,69,64,76)(46,62)(47,57)(48,63)(49,60,74,77)(58,73,68,65);(14,16,28,57,20,31,18,30,21,32,40,62,19,42,41,63)(15,22,44,54,25,47,24,27,26,48,39,55,43,46,52,56)(17,34,68,77,38,61,72,76,37,70,58,60,36,29,35,69)(23,49,65,67,33,64,71,59,51,74,73,53,66,45,50,75);(14,17)(15,23,26,51)(16,29,32,61)(18,35)(19,36)(20,38)(21,37)(22,45)(24,50,52,71)(25,33,43,66)(27,53)(28,58)(30,60,63,77)(31,34,42,70)(39,65,44,73)(40,68)(41,72)(46,74)(47,49)(48,64)(54,59)(55,75)(56,67)(57,76,62,69)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6204);