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×#3567 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
950 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)(15,19)(16,22)(21,26)(23,28)(30,31)(32,35)(33,38)(34,39)(36,40)(37,42)(41,43)(44,45);(15,19)(20,25)(21,26)(27,29)(31,32)(33,40)(37,39)(41,45);(14,15)(16,20)(17,21)(18,19)(22,25)(23,27)(24,26)(28,29)(30,32,35,31)(33,38,40,36)(34,39,42,37)(41,44,45,43);(14,16,18,22)(15,20,19,25)(17,23,24,28)(21,27,26,29)(30,33)(31,36)(32,38)(34,41)(35,40)(37,43)(39,44)(42,45);(14,17,18,24)(15,21,19,26)(16,23,22,28)(20,27,25,29)(30,34)(31,37)(32,39)(33,41)(35,42)(36,43)(38,44)(40,45)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2299);