Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#23622 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | C2×#396 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
960 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,24,19,25,18,23)(16,26,34,37,29,36,28,21)(17,22,31,38,33,39,32,40)(27,41,42,35,30,44,43,45);(14,16,18,28,19,29,20,34)(15,21,24,26,25,37,23,36)(17,30,32,42,33,27,31,43)(22,35,38,44,39,45,40,41);(14,17)(15,22)(16,27)(18,31)(19,33)(20,32)(21,35)(23,38)(24,40)(25,39)(26,41)(28,42)(29,30)(34,43)(36,44)(37,45);(14,18,19,20)(15,23,25,24)(16,28,29,34)(17,31,33,32)(21,36,37,26)(22,38,39,40)(27,42,30,43)(35,44,45,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16610);