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×#3544 |
| 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)(15,18)(16,20)(23,27)(25,33)(28,30)(31,37);(15,18)(19,21)(22,23,26,27)(24,30,32,28)(25,29,33,34)(31,36,37,35);(14,15,17,18)(16,19,20,21);(14,16)(15,19)(17,20)(18,21)(22,24,26,32)(23,28,27,30)(25,31,33,37)(29,35,34,36);(22,25)(23,29)(24,31)(26,33)(27,34)(28,35)(30,36)(32,37)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2276);