Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#32851 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C43×C13 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(19,20)(22,23,26,29)(24,30,32,27)(25,28,34,37)(31,36,33,35)(38,39,42,46)(40,48,50,44)(41,45,43,47)(49,53,51,52);(14,15,18,16)(17,19,21,20)(22,24,26,32)(23,27,29,30)(25,33,34,31)(28,36,37,35)(40,49)(41,43)(44,52)(45,47)(48,53)(50,51);(14,16,18,15)(17,19,21,20)(25,34)(28,37)(31,33)(35,36)(38,40,42,50)(39,44,46,48)(41,49,43,51)(45,52,47,53);(14,17,18,21)(15,19,16,20)(22,25,26,34)(23,28,29,37)(24,31,32,33)(27,35,30,36)(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, 25839);