Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G | |
1938 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)(24,34,36,45)(25,39,42,46)(26,32,27,31)(29,38,44,37)(30,40,47,41)(35,49,50,43)(48,51,53,52);(15,17)(18,19)(20,21)(22,24)(23,29)(25,35)(26,38)(27,37)(28,36)(30,43)(31,45)(32,34)(33,44)(39,53)(40,52)(41,51)(42,50)(46,48)(47,49);(19,21)(22,25,28,42)(23,30,33,47)(24,35,36,50)(26,41,27,40)(29,43,44,49)(31,39,32,46)(34,48,45,53)(37,52,38,51);(24,36)(29,44)(34,45)(35,50)(37,38)(43,49)(48,53)(51,52)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16413);