Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13389 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13389 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2033 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,21)(16,25)(17,19)(18,31)(22,37)(23,40)(24,29)(26,44)(27,32)(28,43)(30,33)(34,42)(35,38)(39,41);(14,15)(16,26)(17,29)(18,23)(19,21)(20,24)(22,28)(25,41)(27,35)(30,45)(31,36)(32,44)(33,40)(34,39)(37,42)(38,43);(14,16,17,27,20,28,19,34)(15,22,21,35,24,26,29,39)(18,32,30,25,33,42,31,43)(23,37,36,41,40,44,45,38)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6377);