Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#33703 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
570 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)(16,19)(17,18)(20,21)(22,23,29,34)(24,35,37,36)(25,41,31,27)(26,42,44,32)(28,45,43,33)(30,46,47,38)(39,49,52,50)(40,48,53,51);(15,18)(19,21)(22,24,27,39,28,40,26,38,29,37,41,52,43,53,44,46)(23,30,32,48,33,49,31,35,34,47,42,51,45,50,25,36);(14,16,17,20)(15,19,18,21)(22,25,26,33,43,42,27,23,29,31,44,45,28,32,41,34)(24,36,38,49,53,51,39,30,37,35,46,50,40,48,52,47);(24,37)(30,47)(35,36)(38,46)(39,52)(40,53)(48,51)(49,50)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26691);