Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#3487 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1536 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,20)(22,30)(24,26)(28,33);(18,19,23,20)(21,26,29,24)(22,25,30,27)(28,32,33,31);(14,15)(16,17)(18,20,23,19)(21,26,29,24)(22,27,30,25)(28,32,33,31);(18,21,23,29)(19,24,20,26)(22,28,30,33)(25,31,27,32);(18,22)(19,25)(20,27)(21,28)(23,30)(24,31)(26,32)(29,33)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2219);