Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#10782 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #386 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
1178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,22,28,24,29,23,27)(20,30,33,41,34,40,32,25)(21,35,37,42,38,43,36,26)(31,39,45,48,46,49,47,44);(18,20,23,32,24,34,22,33)(19,25,27,40,29,41,28,30)(21,31,37,45,38,46,36,47)(26,39,35,48,42,49,43,44);(15,17)(18,21)(19,26)(20,31)(22,36)(23,37)(24,38)(25,39)(27,35)(28,43)(29,42)(30,44)(32,45)(33,47)(34,46)(40,48)(41,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3770);