Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23542 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G | |
1362 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)(14,15)(16,17)(22,23,28,33)(24,34,38,45)(25,39,41,49)(26,32,27,31)(29,37,46,36)(30,43,48,42)(35,51,52,44)(40,47,53,50);(18,19)(20,21)(22,24,28,38)(23,29,33,46)(25,40,41,53)(26,37,27,36)(30,47,48,50)(31,45,32,34)(35,42,52,43)(39,51,49,44);(15,17)(19,21)(22,25,26,42,28,41,27,43)(23,30,31,39,33,48,32,49)(24,35,36,53,38,52,37,40)(29,44,34,50,46,51,45,47);(25,41)(30,48)(35,52)(39,49)(40,53)(42,43)(44,51)(47,50)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16530);