Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32855 |
| 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 ◁ C13×#376 ◁ G | |
510 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)(38,39,42,44)(40,43,48,51)(41,45,49,53)(46,50,47,52);(14,15,18,16)(17,19,21,20)(22,24,26,32)(23,27,29,30)(25,33,34,31)(28,36,37,35)(38,40)(39,43)(41,46)(42,48)(44,51)(45,50)(47,49)(52,53);(14,16,18,15)(17,19,21,20)(25,34)(28,37)(31,33)(35,36)(40,46)(41,49)(43,50)(45,53)(47,48)(51,52);(14,17,18,21)(15,19,16,20)(22,25,26,34)(23,28,29,37)(24,31,32,33)(27,35,30,36)(39,44)(43,51)(45,53)(50,52)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25843);