Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#25931 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C4×Q8×C13 ◁ G | |
1002 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,22,25)(20,24,21,23)(26,27)(28,32)(29,37)(30,39)(31,34)(33,38)(35,41)(36,40);(18,20,22,21)(19,23,25,24)(26,28,31,36)(27,32,34,40)(29,38,35,30)(33,41,39,37);(14,15,16,17)(18,20,22,21)(19,24,25,23)(26,29,30,28,31,35,38,36)(27,32,33,37,34,40,39,41);(18,21,22,20)(19,24,25,23)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18919);