Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13551 |
| subgroup | G/H | |
|---|---|---|
| center | C13×C16 | C42 |
| commutator | C4 | C2×C4×C8×C13 |
| Frattini, cosocle | C2×C16 | C23×C13 |
| socle | C2×C13 | C2×#346 |
| prime radical | C23×C13 | M32 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C13×C16 ◁ G | |
214 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)(14,15,17,22,18,24,32,44,19,25,33,45,35,48,59,70,20,23,34,43,36,46,60,68,37,47,61,69,62,71,76,77)(16,26,28,50,29,51,54,73,30,39,55,42,56,65,74,67,27,49,31,57,52,72,58,75,53,21,38,40,63,41,64,66);(14,16)(15,21,23,39)(17,31)(18,29)(19,30)(20,27)(22,42,43,40)(24,41,46,65)(25,26,47,49)(28,34)(32,58)(33,38)(35,56)(36,52)(37,53)(44,67,68,66)(45,57,69,50)(48,51,71,72)(54,60)(55,61)(59,64)(62,63)(70,75,77,73)(74,76);(16,27)(21,39)(26,49)(28,31)(29,52)(30,53)(38,55)(40,42)(41,65)(50,57)(51,72)(54,58)(56,63)(64,74)(66,67)(73,75)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6539);