Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#1327 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #99 |
| commutator | C2×C4 | C2×C8×C13 |
| Frattini, cosocle | C2×M16 | C22×C13 |
| socle | C2×C13 | #324 |
| prime radical | C23×C13 | M16 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C4×C13 ◁ C2×C13×M16 ◁ G | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,22,18,21,26,28,19,23,25,29,16,20,24,27);(15,20,23,21)(17,25)(22,27,29,28)(24,26)338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 59);