Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C82×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#1273 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C13 | C22 |
| commutator | C2 | C82×C13 |
| Frattini, cosocle | C2×C42 | C22×C13 |
| socle, prime radical | C23×C13 | C42 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C13 ◁ G | |
212 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,20,22,21,23,24,25);(15,17)(26,27,28,30,29,31,32,33)1040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5);