Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19014 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#19030 |
| 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 | |
902 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)(14,19)(20,22)(21,23)(24,25)(26,33)(27,31)(28,37)(29,32)(30,35)(34,38)(36,39);(8,10)(9,14)(11,21)(12,19)(13,20)(15,18)(16,22)(17,23)(24,26,29,36)(25,30,32,38)(27,35,28,34)(31,39,37,33);(8,10)(9,14)(11,19)(12,21)(13,20)(15,22)(16,18)(17,23)(24,25)(26,30)(27,31)(28,37)(29,32)(33,34)(35,39)(36,38);(8,11,13,12)(9,15,17,16)(10,19,20,21)(14,22,23,18)(24,27,29,28)(25,31,32,37)(26,34,36,35)(30,33,38,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12018);