Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#2103 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C23×C13 |
| socle | C2×C13 | #400 |
| prime radical | C23×C13 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
148 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,23,19,24,20,35)(16,25,27,37,29,40,28,21)(17,30,32,44,33,22,34,39)(26,38,41,45,42,43,31,36);(14,16,20,27,19,29,18,28)(15,21,35,25,24,37,23,40)(17,31,34,26,33,41,32,42)(22,38,44,45,30,43,39,36);(14,17,18,32,19,33,20,34)(15,22,23,39,24,30,35,44)(16,26,27,41,29,42,28,31)(21,36,25,38,37,45,40,43)338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 835);