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×C4 |
| direct product | C13×#2821 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| prime radical | C24×C13 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,21,23)(20,22,24,25)(27,31)(32,34)(33,37)(40,41);(15,17)(20,24)(22,25)(26,27)(28,34)(29,37)(30,31)(32,36)(33,39)(35,40)(38,41);(14,15)(16,17)(18,19)(20,22)(21,23)(24,25)(26,28,30,36)(27,32,31,34)(29,38,39,35)(33,41,37,40);(18,20)(19,22)(21,24)(23,25)(26,29,30,39)(27,33,31,37)(28,35,36,38)(32,40,34,41)338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1553);