Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19621 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#19650 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3184 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
720 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,16)(11,20)(12,14)(13,19)(15,17)(18,22)(21,23)(24,25)(26,33)(27,31)(28,37)(29,32)(30,35)(34,38)(36,39);(8,10,17,23,12,18,11,19)(9,13,20,22,14,21,15,16);(9,14)(13,21)(15,20)(16,22)(24,26,27,34,29,36,28,35)(25,30,37,39,32,38,31,33);(10,18)(13,21)(16,22)(19,23)(24,27,29,28)(25,31,32,37)(26,34,36,35)(30,33,38,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12638);