Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33657 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33657 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
566 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)(16,24)(17,27)(18,30)(20,33)(22,37)(23,36)(25,41)(26,29)(28,43)(31,44)(32,42)(34,40)(35,38)(39,45);(14,15)(16,20)(17,28)(18,23)(19,21)(22,31)(24,40)(25,34)(26,35)(27,43)(29,45)(30,36)(32,39)(33,41)(37,44)(38,42);(14,16,18,32,19,25,30,26)(15,20,23,39,21,34,36,35)(17,29,27,41,31,42,44,24)(22,38,37,40,28,45,43,33);(15,21)(20,34)(22,28)(23,36)(33,40)(35,39)(37,43)(38,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26645);