Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#9812 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #390 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C2×C13×#127 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
470 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)(15,16)(17,18)(20,21)(22,23,25,29,26,28,30,36)(24,27,32,35,31,34,33,37);(14,15,17,16,19,21,18,20)(22,24,30,32,26,31,25,33)(23,27,29,37,28,34,36,35);(14,16,17,21,19,20,18,15)(24,31)(27,34)(32,33)(35,37)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2800);