Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#3026 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C24×C13 ◁ G | |
800 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 212 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 — 4 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,20)(18,21)(22,28)(23,26)(24,27)(25,29);(14,16)(15,19)(17,22)(18,23)(20,25)(21,26)(24,29)(27,28);(14,17)(15,20)(16,22)(18,24)(19,25)(21,27)(23,29)(26,28);(15,21)(19,26)(20,27)(25,28)377 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1758);