Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23914 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3485 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1706 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)(18,19,23,27)(20,24,29,39)(21,31,32,43)(22,34,37,26)(25,36,41,33)(28,44,45,48)(30,42,35,40)(38,47,49,46);(14,15)(16,17)(18,20,23,29)(19,24,27,39)(21,28,32,45)(22,35,37,30)(25,38,41,49)(26,42,34,40)(31,48,43,44)(33,47,36,46);(15,17)(18,21)(19,25)(20,28)(22,36)(23,32)(24,38)(26,43)(27,41)(29,45)(30,47)(31,34)(33,37)(35,46)(39,49)(40,48)(42,44);(20,29)(22,37)(24,39)(26,34)(28,45)(31,43)(33,36)(38,49)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16902);