Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#2513 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| prime radical | C22×D4×C13 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
440 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,16)(17,20,21,19)(23,26)(24,28)(30,31,34,37)(32,36,33,35);(15,16)(19,20)(22,23,25,26)(24,27,28,29)(30,32,34,33)(31,35,37,36);(14,16,18,15)(17,20,21,19)(22,23)(24,27)(25,26)(28,29)(30,31)(32,35)(33,36)(34,37);(14,17,18,21)(15,19,16,20)(22,24,25,28)(23,27,26,29)(30,33,34,32)(31,36,37,35)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1245);