Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25142 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
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)(18,19,22,26,23,27,36,43)(20,24,29,38,30,39,47,49)(21,31,33,41,34,42,35,25)(28,44,45,40,32,48,46,37);(15,17)(18,20,22,29,23,30,36,47)(19,24,26,38,27,39,43,49)(21,32,33,46,34,28,35,45)(25,40,31,48,41,37,42,44);(18,21,23,34)(19,25,27,41)(20,28,30,32)(22,35,36,33)(24,37,39,40)(26,42,43,31)(29,46,47,45)(38,48,49,44);(15,17)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18130);