Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#2064 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C13 |
| prime radical | C23×C13 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
208 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,22,29,24,28,23,27)(20,26,30,25,21,32,31,33);(14,15)(16,17)(18,20,22,30,24,21,23,31)(19,25,27,26,28,33,29,32);(15,17)(18,21,24,20)(19,26,28,32)(22,30,23,31)(25,29,33,27)338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 796);