Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#1416 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C13 | D16 |
| commutator | C16 | C2×C4×C13 |
| Frattini, cosocle | C2×C16 | C22×C13 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C4×C13 ◁ C2×C8×C13 ◁ C2×C13×C16 ◁ G | |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(19,24)(20,28)(21,30)(22,34)(25,40)(26,43)(27,39)(29,33)(31,47)(32,37)(35,41)(36,38)(42,48)(44,45)(46,49);(18,19,23,27)(20,29,32,46)(21,33,35,49)(22,36,34,26)(24,37,39,28)(25,41,42,30)(31,48,44,40)(38,45,43,47)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 148);