Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25186 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×2−1+4 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
974 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19,23,28)(20,29,33,25)(21,34,36,43)(22,24,38,27)(26,37,42,35)(30,39,32,41)(31,46,47,49)(40,45,44,48);(14,16,17,15)(19,24)(20,30)(22,38)(26,34)(27,28)(31,45)(32,33)(35,37)(39,41)(42,43)(46,49)(47,48);(15,16)(18,20,23,33)(19,25,28,29)(21,31,36,47)(22,32,38,30)(24,39,27,41)(26,40,42,44)(34,49,43,46)(35,45,37,48);(18,21)(19,26)(20,31)(22,37)(23,36)(24,34)(25,40)(27,43)(28,42)(29,44)(30,45)(32,48)(33,47)(35,38)(39,49)(41,46)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18174);