Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36679 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
1506 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23)(24,26)(25,27)(28,29)(30,31,34,37)(32,38,40,35)(33,36,41,43)(39,44,45,42);(24,28)(26,29)(30,32,34,40)(31,35,37,38)(33,39,41,45)(36,42,43,44);(15,18)(19,21)(22,24)(23,26)(25,28)(27,29)(30,33,34,41)(31,36,37,43)(32,39,40,45)(35,42,38,44);(23,27)(24,28)(33,41)(36,43)(39,45)(42,44);(14,16,17,20)(15,19,18,21)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29667);