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×#3565 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| 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)(14,15,18,19)(16,22,23,20)(17,25,26,21)(24,27,29,28)(30,31)(32,37)(33,38)(34,42)(35,36)(39,43)(40,41)(44,45);(15,19)(16,23)(21,25)(24,29)(31,36)(33,37)(39,42)(41,44);(14,16,18,23)(15,20,19,22)(17,24,26,29)(21,27,25,28)(30,32,35,38)(31,37,36,33)(34,40,43,45)(39,44,42,41);(14,15)(16,20)(17,21)(18,19)(22,23)(24,27)(25,26)(28,29)(30,33,35,37)(31,38,36,32)(34,41,43,44)(39,45,42,40);(14,17,18,26)(15,21,19,25)(16,24,23,29)(20,27,22,28)(30,34,35,43)(31,39,36,42)(32,40,38,45)(33,41,37,44)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2297);