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×#3500 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1540 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)(18,19)(20,26)(21,29)(22,23)(24,28)(25,30)(27,31)(32,33);(19,23)(24,26)(25,29)(31,32);(14,15,16,17)(18,20)(19,24)(21,27)(22,28)(23,26)(25,31)(29,32)(30,33);(18,19)(20,24)(21,25)(22,23)(26,28)(27,31)(29,30)(32,33);(18,21,22,30)(19,25,23,29)(20,27,28,33)(24,31,26,32)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2232);