Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#2971 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C24 |
| commutator | C22 | C23×C4×C13 |
| Frattini, cosocle | C2×C4 | C24×C13 |
| socle | C22×C13 | C23×C4 |
| prime radical | C2×C13×#41 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ G | |
402 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 276 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23,27,24,26,28,25,29);(15,18)(19,21)(23,28)(24,29);(22,24,27,28,26,29,25,23);(14,16,17,20)(15,19,18,21)(22,25,26,27)(23,24,28,29)650 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1703);