Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#22123 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C13×#376 ◁ G | |
740 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(19,22)(20,24)(26,27)(28,35)(29,33)(30,32)(31,36)(34,38)(37,39)(40,41);(14,16,17,15)(18,19)(20,23)(21,22)(24,25)(26,28)(27,31)(29,36)(30,37)(32,40)(33,35)(34,39)(38,41);(19,22)(23,25)(27,32)(28,36)(30,38)(31,39)(33,34)(35,40);(18,20,21,24)(19,23,22,25)(27,33)(28,36)(32,34)(37,41)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15111);