Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#1377 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22⋊C4 |
| commutator | C22 | C4×C8×C13 |
| Frattini, cosocle | C22×C8 | C22×C13 |
| socle | C22×C13 | C22⋊C8 |
| prime radical | C23×C13 | C2×C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C8×C13 ◁ G | |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,20,24,21,25,27,31,22,23,26,29,28,30,32,33);(14,15,16,17)(19,23)(20,26)(25,30)(27,32)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 109);