Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#2956 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C22×D4 |
| commutator | C4 | C23×C4×C13 |
| Frattini, cosocle | C2×C4 | C24×C13 |
| socle | C2×C13 | C2×C4×D4 |
| prime radical | C13×#575 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C13×M16 ◁ G | |
458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,22,19,16,23,21)(17,20,26,28,25,24,29,27);(14,16)(15,19)(17,24)(18,21)(20,25)(22,23)(26,27)(28,29);(14,17,18,26,19,25,23,29)(15,20,22,28,16,24,21,27);(17,25)(20,24)(26,29)(27,28)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1688);