Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#3552 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1004 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,21)(23,28)(24,25)(26,34)(36,37);(15,19)(16,20)(22,23,27,28)(24,30,25,29)(26,31,34,35)(32,37,33,36);(22,24,27,25)(23,29,28,30)(26,32,34,33)(31,36,35,37);(14,16,18,20)(15,17,19,21)(22,25,27,24)(23,30,28,29)(26,33,34,32)(31,37,35,36);(14,17)(15,20)(16,19)(18,21)(22,26)(23,31)(24,32)(25,33)(27,34)(28,35)(29,36)(30,37)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2284);