Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#3521 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1042 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)(19,21)(22,23)(24,30)(25,33)(26,27)(28,32)(29,34)(31,35)(36,37);(23,27)(28,30)(29,33)(35,36);(14,15)(16,19)(17,18)(20,21)(22,24,26,32)(23,28,27,30)(25,31,34,37)(29,35,33,36);(22,23)(24,28)(25,29)(26,27)(30,32)(31,35)(33,34)(36,37);(14,16,17,20)(15,19,18,21)(22,25)(23,29)(24,31)(26,34)(27,33)(28,35)(30,36)(32,37)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2253);