Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12784 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | C23 |
| commutator | C23 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C23×C13 | C22×C8 |
| prime radical | C24×C13 | C2×C8 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ G | |
478 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19)(20,21)(22,23,25,29,26,30,35,41,27,31,36,42,37,43,47,51)(24,28,33,39,34,40,46,50,32,38,44,48,45,49,52,53);(14,15,16,17)(22,24)(23,28)(25,33)(26,34)(27,32)(29,39)(30,40)(31,38)(35,46)(36,44)(37,45)(41,50)(42,48)(43,49)(47,52)(51,53);(19,21)(24,32)(28,38)(33,44)(34,45)(39,48)(40,49)(46,52)(50,53)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5772);