Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33829 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#2218 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(22,23,25,30)(24,33,34,28)(26,29,37,45)(27,40,38,32)(31,47,46,39)(35,41,50,44)(36,43,51,49)(42,53,48,52);(14,15)(16,19)(17,18)(20,21)(22,24,25,34)(23,28,30,33)(26,35,37,50)(27,36,38,51)(29,44,45,41)(31,42,46,48)(32,43,40,49)(39,53,47,52);(15,18)(19,21)(23,29)(24,34)(26,39)(27,38)(28,41)(30,45)(31,32)(33,44)(35,52)(37,47)(40,46)(42,49)(43,48)(50,53);(14,16,17,20)(15,19,18,21)(23,30)(24,34)(29,45)(31,46)(32,40)(35,50)(36,51)(52,53)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26817);