Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#3046 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| prime radical | C2×C13×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ G | |
472 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,23,27)(20,24,29,33)(21,26,22,31)(25,30,32,28);(14,15,16,17)(18,20)(19,24)(21,30)(22,28)(23,29)(25,31)(26,32)(27,33);(18,20)(19,25)(21,28)(22,30)(23,29)(24,31)(26,33)(27,32);(18,21,23,22)(19,26,27,31)(20,28,29,30)(24,25,33,32)416 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1778);