Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#13157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1936 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | #137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
296 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)(14,15,20,27,22,28,21,50)(16,29,33,52,34,61,48,62)(17,35,39,57,40,63,49,71)(18,41,19,45,44,26,43,25)(23,32,53,31,55,46,54,42)(24,37,58,38,60,72,59,47)(30,65,68,76,69,51,36,56)(64,73,74,67,77,66,75,70);(14,16,18,42,21,33,43,32,22,34,44,31,20,48,19,46)(15,23,45,29,27,54,26,62,28,55,25,61,50,53,41,52)(17,36,72,67,39,69,47,73,40,68,37,70,49,30,38,66)(24,56,57,75,59,65,35,64,60,76,71,74,58,51,63,77);(14,17,18,37,21,39,43,38,22,40,44,72,20,49,19,47)(15,24,25,57,27,59,41,35,28,60,45,71,50,58,26,63)(16,30,31,66,33,36,46,67,34,69,42,73,48,68,32,70)(23,51,29,64,54,56,62,74,55,65,61,77,53,76,52,75)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6145);