Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#18005 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C13×#449 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C4×C13×M16 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
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)(16,23)(17,22)(18,26)(19,21)(20,24)(25,29)(27,28)(30,31,33,36,34,37,40,43)(32,35,39,42,38,41,44,45);(14,16,19,25)(15,20,21,28)(17,24,18,27)(22,29,26,23);(15,21)(20,28)(22,26)(23,29)(30,32,33,39,34,38,40,44)(31,35,36,42,37,41,43,45);(14,17,19,18)(15,22,21,26)(16,24,25,27)(20,29,28,23)(32,38)(35,41)(39,44)(42,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10993);