Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3061 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
890 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)(18,19,22,25,24,29,23,28)(20,30,31,26,34,41,33,42)(21,35,36,27,38,39,37,43)(32,40,45,48,47,49,46,44);(14,15)(16,17)(19,25,29,28)(20,31,34,33)(27,39,43,35)(32,45,47,46);(15,17)(18,20)(19,26)(21,32)(22,33)(23,31)(24,34)(25,30)(27,40)(28,41)(29,42)(35,48)(36,46)(37,45)(38,47)(39,44)(43,49);(18,21,23,37,24,38,22,36)(19,27,25,39,29,43,28,35)(20,32,31,45,34,47,33,46)(26,40,30,44,42,49,41,48)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18430);