Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33388 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C22×#102 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3584 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
1128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20,22,34)(17,27)(18,30)(21,33,36,44)(23,28,31,35)(25,40)(26,39)(29,32)(37,41,42,45)(38,43);(14,15)(16,21)(17,28)(18,31)(19,22)(20,32)(23,30)(24,36)(25,41)(26,42)(27,34)(29,35)(33,43)(37,39)(38,45)(40,44);(14,16)(15,21)(17,25)(18,26)(19,24)(20,33)(22,36)(23,37)(27,40)(28,41)(29,38)(30,39)(31,42)(32,43)(34,44)(35,45);(16,24)(21,36)(25,38)(26,39)(33,44)(37,42)(40,43)(41,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26376);