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×#3511 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,20)(24,28)(26,29);(14,15,18,17)(16,20,21,19)(22,23,25,27)(24,26,28,29);(14,15,18,17)(16,19,21,20)(22,24,25,28)(23,26,27,29);(14,16,18,21)(15,19,17,20);(14,17,18,15)(16,20,21,19)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2243);