Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#22645 |
| 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 | |
658 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)(15,19)(20,21)(22,23)(24,26)(25,27)(28,29)(30,31,33,37,34,36,40,43)(32,35,39,42,38,41,44,45);(14,15,18,19)(16,20,17,21)(22,24,25,28)(23,26,27,29)(32,38)(35,41)(39,44)(42,45);(14,16,18,17)(15,20,19,21)(23,27)(26,29)(30,32)(31,35)(33,39)(34,38)(36,41)(37,42)(40,44)(43,45);(14,17,18,16)(15,20,19,21)(31,36)(32,38)(37,43)(39,44)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15633);