Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#2952 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D4 |
| commutator | C4 | C23×C4×C13 |
| Frattini, cosocle | C2×C4 | C24×C13 |
| prime radical | C2×C13×#135 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ G | |
484 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19,24,29)(20,30,21,26)(22,28,23,27)(25,32,33,31);(18,20,24,21)(19,25,29,33)(22,31,23,32)(26,27,30,28);(14,16,17,15)(18,21,24,20)(19,26,29,30)(22,31,23,32)(25,27,33,28);(18,22,24,23)(19,27,29,28)(20,31,21,32)(25,30,33,26)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1684);