Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#2238 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C13 |
| prime radical | C13×#469 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×M16 ◁ G | |
134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 208 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19)(16,22)(17,25)(20,27)(21,24)(23,29)(26,28);(16,23)(19,27)(22,29)(24,28);(14,15,17,26,18,20,25,21)(16,24,22,27,23,28,29,19)260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 970);