Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33495 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C24 |
| commutator | C22 | C23×C8×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C22×C13 | C23×C8 |
| prime radical | C13×#532 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ G | |
564 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)(16,20)(17,19)(18,21)(22,23,26,31,27,32,38,46,25,30,36,44,37,45,49,53)(24,29,34,42,35,43,48,52,33,28,39,40,47,41,50,51);(14,16)(15,18)(17,21)(19,20)(22,24)(23,28)(25,33)(26,34)(27,35)(29,30)(31,40)(32,41)(36,39)(37,47)(38,48)(42,44)(43,45)(46,51)(49,50)(52,53);(16,21)(18,20)(22,24)(23,29)(25,33)(26,34)(27,35)(28,30)(31,42)(32,43)(36,39)(37,47)(38,48)(40,44)(41,45)(46,52)(49,50)(51,53);(15,19)(18,20)(23,30)(24,33)(31,44)(32,45)(34,39)(35,47)(46,53)(48,50)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26483);