Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2218 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C4 |
| direct product | C13×#2244 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C13 |
| prime radical | C13×#493 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ C4×C8×C13 ◁ G | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(23,29)(24,35)(25,30)(26,37)(27,31)(32,33)(34,36);(15,18)(19,21)(22,23,30,24,27,33,37,36,28,34,26,32,31,35,25,29);(14,16,17,20)(15,19,18,21)(22,24,25,23,31,29,26,35,28,32,37,34,27,36,30,33)338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 976);