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×#33835 |
| 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 | |
670 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)(18,19,24,21)(20,28,32,47)(22,35,39,46)(23,34,37,27)(25,42,29,31)(26,41,33,38)(30,48,40,44)(36,45,49,43);(18,20,24,32)(19,25,21,29)(22,36,39,49)(23,40,37,30)(26,44,33,48)(27,45,34,43)(28,46,47,35)(31,41,42,38);(15,17)(18,21,24,19)(20,29,32,25)(22,33,39,26)(23,34,37,27)(28,31,47,42)(30,45,40,43)(35,38,46,41)(36,48,49,44);(18,22)(19,26)(20,30)(21,33)(23,41)(24,39)(25,43)(27,46)(28,47)(29,45)(31,42)(32,40)(34,35)(37,38)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26823);