Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C8 |
| direct product | C13×#1455 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C13 | C23 |
| commutator | C22 | C2×C42×C13 |
| Frattini, cosocle | C42 | C23×C13 |
| socle | C22×C13 | C2×C42 |
| prime radical | C23×C13 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C13 ◁ G | |
214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,19,17,18,20,21);(22,23,24,27,25,26,28,29);(15,18)(19,21)(23,26)(27,29)728 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 187);