Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#2501 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| prime radical | C2×C13×#121 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
708 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 248 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)(15,16)(19,20)(22,23,26,28)(24,25,27,29);(14,15,17,16)(18,19,21,20)(22,24)(23,25)(26,27)(28,29);(18,19,21,20)(22,25)(23,27)(24,28)(26,29);(14,16,17,15)(18,20,21,19)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1233);