Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#10375 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
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)(24,30,32,36)(25,28)(26,29)(27,33,31,34)(35,37);(22,23)(24,31,32,27)(25,28)(26,29)(30,33,36,34)(35,37);(14,15,17,19)(16,21,20,18)(22,24)(23,27)(25,34)(26,32)(28,36)(29,31)(30,37)(33,35)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3363);