Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33836 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3285 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
664 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)(19,24)(20,28)(21,32)(22,35)(25,42)(26,46)(27,41)(29,45)(30,43)(31,38)(33,37)(36,39)(40,44)(47,48);(18,19,23,27)(20,29,31,42)(21,33,36,46)(22,37,35,26)(24,39,41,32)(25,43,45,30)(28,48,38,40)(34,47,49,44);(15,17);(18,20,23,31)(19,25,27,45)(21,34,36,49)(22,38,35,28)(24,40,41,48)(26,47,37,44)(29,46,42,33)(30,39,43,32)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26824);