Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#20713 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #381 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | C2×#381 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
1244 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)(14,15,19,25,20,24,18,23)(16,26,28,39,29,21,34,36)(17,30,33,37,32,22,31,38)(27,35,41,44,42,40,43,45);(14,16)(15,21)(17,27)(18,28)(19,34)(20,29)(22,35)(23,36)(24,26)(25,39)(30,40)(31,41)(32,42)(33,43)(37,44)(38,45);(14,17)(15,22,24,30)(16,27)(18,31)(19,33)(20,32)(21,35,26,40)(23,37,25,38)(28,41)(29,42)(34,43)(36,44,39,45);(14,18,20,19)(15,23,24,25)(16,28,29,34)(17,31,32,33)(21,36,26,39)(22,37,30,38)(27,41,42,43)(35,44,40,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13701);