Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#23382 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C23×C13 | C23×C4 |
| prime radical | C24×C13 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
606 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)(16,20)(17,18)(19,21)(22,23,25,27)(24,26,29,28)(30,31,34,37,33,35,40,42)(32,36,39,43,38,41,44,45);(14,15)(16,19)(17,18)(20,21)(22,23)(24,28)(25,27)(26,29)(31,35)(36,41)(37,42)(43,45);(15,18)(19,20)(22,24,25,29)(23,26,27,28)(30,32,33,38)(31,36,35,41)(34,39,40,44)(37,43,42,45);(14,16,17,21)(15,19,18,20)(23,27)(26,28)(31,35)(32,38)(37,42)(39,44)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16370);