Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#2833 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(19,21)(22,23,26,27)(24,28,29,25)(31,35)(36,38)(37,41)(44,45);(16,20)(19,21)(24,29)(25,28)(30,31,34,35)(32,38,40,36)(33,41,43,37)(39,44,42,45);(14,15)(16,19)(17,18)(20,21)(22,24)(23,25)(26,29)(27,28)(30,32,34,40)(31,36,35,38)(33,42,43,39)(37,45,41,44);(14,16)(15,19)(17,20)(18,21)(22,25)(23,24)(26,28)(27,29)(30,33,34,43)(31,37,35,41)(32,39,40,42)(36,44,38,45)338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1565);