Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C13 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×C13×#95 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C13 | C22 |
| commutator | C2 | C43×C13 |
| Frattini, cosocle | C24 | C23×C13 |
| socle, prime radical | C24×C13 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C13 ◁ G | |
752 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4)(17,18,19,20,21,22,23,24,25,26,27,28,29);(10,12)(13,14,16,15);(5,6,7,8)(9,10,11,12)(13,15,16,14)1040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 164);