Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#21671 |
| 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 | |
676 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)(16,21)(17,19)(18,20)(22,23)(24,26)(25,27)(28,29)(30,31,34,33,35,37,43,42)(32,36,40,41,38,44,45,39);(14,16,18,17)(15,19,20,21)(22,24,25,28)(23,26,27,29)(30,32)(31,36)(33,41)(34,40)(35,38)(37,44)(39,42)(43,45);(14,17,18,16)(15,19,20,21)(23,27)(26,29)(32,38)(36,44)(39,41)(40,45);(30,33,34,37,35,42,43,31)(32,39,40,36,38,41,45,44)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14659);