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×#3539 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1050 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
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)(22,23)(24,27)(25,30)(26,31)(28,32)(29,34)(33,35)(36,37);(15,18)(19,21)(23,24)(25,32)(29,31)(33,37);(14,15)(16,19)(17,18)(20,21)(22,24,27,23)(25,30,32,28)(26,31,34,29)(33,36,37,35);(14,16)(15,19)(17,20)(18,21)(22,25)(23,28)(24,30)(26,33)(27,32)(29,35)(31,36)(34,37);(22,26,27,34)(23,29,24,31)(25,33,32,37)(28,35,30,36)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2271);