Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33613 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3061 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,23,28)(20,30,33,46)(21,36,37,26)(22,40,42,47)(24,43,41,29)(25,44,39,34)(27,45,32,31)(35,49,48,38);(18,20,31,36,24,35,42,44,23,33,45,26,41,48,22,34)(19,25,40,38,29,21,32,46,28,39,47,49,43,37,27,30);(15,17)(18,21)(19,26)(20,32)(22,38)(23,37)(24,39)(25,41)(27,33)(28,36)(29,34)(30,45)(31,46)(35,47)(40,48)(42,49)(43,44);(20,33)(21,37)(25,39)(26,36)(30,46)(34,44)(35,48)(38,49)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26601);