Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10518 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#10521 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,21)(16,18,20,17)(22,23,27,31)(24,25,29,35)(26,32,37,30)(28,36,34,33);(15,16)(17,18)(20,21)(22,24)(23,28)(25,32)(26,36)(27,29)(30,35)(31,34)(33,37);(14,16,18,21,19,20,17,15)(22,25,26,34,27,35,37,28)(23,29,30,36,31,24,32,33)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3509);