Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#3290 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ G | |
454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,25)(17,22)(18,35)(19,24)(20,28)(21,33)(23,36)(26,38)(27,44)(29,40)(30,39)(31,37)(32,42)(34,41)(43,45);(14,16)(15,20)(17,31)(18,29)(19,30)(21,38)(22,43)(23,39)(24,40)(25,35)(26,34)(27,32)(28,36)(33,45)(37,42)(41,44);(14,17)(15,21)(16,26)(18,32)(19,34)(20,37)(22,35)(23,41)(24,42)(25,44)(27,28)(29,45)(30,31)(33,36)(38,40)(39,43);(14,17)(15,22)(16,27)(18,33)(19,34)(20,38)(21,35)(23,42)(24,41)(25,44)(26,28)(29,31)(30,45)(32,36)(37,40)(39,43)377 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2022);