Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10013 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #392 |
| prime radical | C13×#3100 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
598 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)(15,18)(16,20)(19,21)(22,23)(24,30)(25,33)(26,29)(27,31)(28,35)(32,37)(34,36);(14,15,17,19)(16,21,20,18)(22,24,26,32)(23,27,29,36)(25,34,35,31)(28,37,33,30);(14,15)(16,21)(17,19)(18,20)(27,36)(30,37)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3001);