Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C27 |
| direct product | C4×C13×#394 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C13 | C23 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C24 | C24×C13 |
| socle | C24×C13 | C24 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C13 ◁ G | |
2550 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4)(17,18,19,20,21,22,23,24,25,26,27,28,29);(10,12)(13,14)(15,16);(6,8)(10,12)(14,15);(5,6)(7,8)(9,10)(11,12)(13,15,16,14)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6846);