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×#33843 |
| 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 | |
668 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)(25,40)(26,43)(27,46)(29,42)(30,44)(31,38)(33,37)(36,39)(41,45)(47,48);(18,19,23,25)(20,29,31,43)(21,33,36,46)(22,37,35,27)(24,39,40,32)(26,44,42,30)(28,48,38,41)(34,47,49,45);(15,17)(19,25)(24,40)(26,42)(27,37)(29,43)(33,46)(41,48)(45,47);(18,20,23,31)(19,26,25,42)(21,34,36,49)(22,38,35,28)(24,41,40,48)(27,47,37,45)(29,46,43,33)(30,39,44,32)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26831);