Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32791 |
| 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 ◁ C22×C42×C13 ◁ G | |
628 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)(16,18)(17,19)(20,21)(22,23,27,30)(24,31,25,28)(26,29,34,37)(32,36,33,35)(38,39,42,46)(40,48,50,44)(41,45,43,47)(49,53,51,52);(14,16)(15,18)(17,20)(19,21)(22,24,27,25)(23,28,30,31)(26,33,34,32)(29,36,37,35)(40,49)(41,43)(44,52)(45,47)(48,53)(50,51);(15,19)(18,21)(22,25,27,24)(23,28,30,31)(26,32,34,33)(29,36,37,35)(38,40)(39,44)(41,49)(42,50)(43,51)(45,52)(46,48)(47,53);(16,20)(18,21)(22,26,27,34)(23,29,30,37)(24,32,25,33)(28,35,31,36)(38,41,42,43)(39,45,46,47)(40,49,50,51)(44,52,48,53)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25779);