Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19050 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#19061 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
942 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)(10,18)(11,15)(12,16)(13,17)(14,20)(19,22)(21,23)(24,25)(26,33)(27,31)(28,36)(29,32)(30,34)(35,38)(37,39);(8,10)(9,14)(11,19)(12,20)(13,21)(15,18)(16,23)(17,22)(24,26,29,35)(25,30,32,39)(27,34,28,37)(31,38,36,33);(8,10)(9,14)(11,20)(12,19)(13,21)(15,23)(16,18)(17,22)(27,28)(31,36)(33,38)(34,37);(8,11,13,12)(9,15,17,16)(10,19,21,20)(14,18,22,23)(24,27,29,28)(25,31,32,36)(26,34,35,37)(30,38,39,33)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12049);