Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#3557 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| prime radical | C13×#540 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,21)(17,22)(18,26)(19,20)(23,27)(24,25)(28,29)(31,35)(32,38)(33,41)(43,45);(15,20)(17,21)(23,26)(25,28)(30,31,34,35)(32,39,38,36)(33,37,41,42)(40,45,44,43);(14,16,19,22)(15,21,20,17)(18,24,27,29)(23,28,26,25)(30,31)(32,36)(33,37)(34,35)(38,39)(40,43)(41,42)(44,45);(14,17,19,21)(15,22,20,16)(18,25,27,28)(23,29,26,24)(30,32,34,38)(31,36,35,39)(33,40,41,44)(37,43,42,45);(14,18,19,27)(15,23,20,26)(16,24,22,29)(17,25,21,28)(30,33,34,41)(31,37,35,42)(32,40,38,44)(36,43,39,45)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2289);