Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#3069 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#121 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| prime radical | C13×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
446 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)(14,15,20,25)(16,26,28,37)(17,31,33,39)(18,24,19,23)(21,30,36,29)(22,34,38,32)(27,41,42,35)(40,44,45,43);(14,16,18,29,20,28,19,30)(15,21,23,26,25,36,24,37)(17,27,32,43,33,42,34,44)(22,35,31,40,38,41,39,45);(14,17)(15,22)(16,27)(18,32)(19,34)(20,33)(21,35)(23,31)(24,39)(25,38)(26,40)(28,42)(29,43)(30,44)(36,41)(37,45);(16,28)(21,36)(26,37)(27,42)(29,30)(35,41)(40,45)(43,44)377 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1801);