Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#10996 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C24 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #379 |
| prime radical | C13×#3449 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
1306 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)(18,19,22,27,23,26,35,40)(20,28,31,41,30,24,34,37)(21,25,33,38,32,39,45,49)(29,36,44,47,43,42,46,48);(14,15)(16,17)(18,20)(19,24)(21,29)(22,34)(23,30)(25,36)(26,28)(27,41)(31,35)(32,43)(33,46)(37,40)(38,48)(39,42)(44,45)(47,49);(15,17)(18,21)(19,25)(20,29)(22,33)(23,32)(24,36)(26,39)(27,38)(28,42)(30,43)(31,44)(34,46)(35,45)(37,47)(40,49)(41,48)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3984);