Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33850 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
686 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)(18,19,25,21)(20,30,32,45)(22,36,39,28)(23,35,42,27)(24,37,41,29)(26,38,31,33)(34,48,43,46)(40,47,49,44);(18,20,25,32)(19,26,21,31)(22,38,39,33)(23,40,42,49)(24,43,41,34)(27,45,35,30)(28,46,36,48)(29,47,37,44);(15,17)(18,21,25,19)(20,31,32,26)(22,35,39,27)(23,36,42,28)(24,37,41,29)(30,33,45,38)(34,47,43,44)(40,48,49,46);(18,22)(19,27)(20,32)(21,35)(23,41)(24,42)(25,39)(26,31)(28,37)(29,36)(30,48)(33,49)(38,40)(45,46)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26838);