Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#2165 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #117 |
| commutator | C2×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C8 | C23×C13 |
| socle | C2×C13 | #432 |
| prime radical | C23×C13 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C13×#97 ◁ G | |
128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,21,17,22,24,29,18,19,23,26,25,20,27,28);(15,19)(16,23)(20,22)(24,27);(15,20,19,22)(16,23)(21,29,26,28)(24,27)416 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 897);