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×#3555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| prime radical | C13×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
910 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)(14,15,19,22)(16,17,24,20)(18,26,27,21)(23,28,29,25)(30,31,34,37)(32,35,40,38)(33,41,42,36)(39,44,45,43);(14,16,19,24)(15,20,22,17)(18,23,27,29)(21,28,26,25)(30,31)(32,38)(33,36)(34,37)(35,40)(39,44)(41,42)(43,45);(14,17,19,20)(15,16,22,24)(18,25,27,28)(21,23,26,29);(14,16)(15,20)(17,22)(18,23)(19,24)(21,28)(25,26)(27,29)(30,32)(31,35)(33,39)(34,40)(36,43)(37,38)(41,44)(42,45);(14,18,19,27)(15,21,22,26)(16,23,24,29)(17,25,20,28)(30,33,34,42)(31,36,37,41)(32,39,40,45)(35,43,38,44)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2287);