Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C210 |
| direct product | C13×#34632 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
5346 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,27)(25,29)(26,28)(30,33)(31,34)(32,35)(36,37);(15,17)(22,24)(23,27)(25,31)(26,30)(28,33)(29,34)(32,36)(35,37);(19,21)(24,30)(27,33)(31,36)(34,37);(23,28)(27,33)(29,35)(34,37);(22,25,26,32)(23,29,28,35)(24,31,30,36)(27,34,33,37)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27620);