Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19651 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#19670 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
746 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)(8,9,13,16)(10,17,15,12)(11,14,19,21)(18,23,22,20)(24,25)(26,33)(27,32)(28,30)(29,37)(31,36)(34,38)(35,39);(8,10,12,9,13,15,17,16)(11,18,20,14,19,22,23,21)(25,30)(31,38)(32,37)(33,39);(8,11)(9,14)(10,18)(12,20)(13,19)(15,22)(16,21)(17,23)(24,26,29,36,28,35,27,34)(25,31,32,33,30,38,37,39);(11,19)(14,21)(18,22)(20,23)(24,27,28,29)(25,32,30,37)(26,34,35,36)(31,33,38,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12658);