Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26990 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#537 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
766 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,19)(18,21)(22,23)(24,30)(25,38)(26,41)(27,34)(28,33)(29,36)(31,42)(32,39)(35,49)(37,45)(40,44)(43,48)(46,50)(47,53)(51,52);(14,16,17,21)(15,18,19,20)(22,24,27,36,28,25,39,37)(23,29,32,30,33,45,34,38)(26,35,42,50,43,40,53,51)(31,44,41,46,47,49,48,52);(15,19)(18,20)(22,25)(23,30)(24,28)(26,40)(27,37)(29,34)(31,46)(32,45)(33,38)(35,43)(36,39)(41,49)(42,51)(44,48)(47,52)(50,53);(15,19)(18,20)(22,26,39,53,28,43,27,42)(23,31,34,48,33,47,32,41)(24,35,37,51,25,40,36,50)(29,44,38,52,45,49,30,46)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19978);