Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18934 |
| 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 | |
1020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,15)(11,16)(12,21)(13,17)(14,18)(19,22)(20,23)(24,25)(26,34)(27,32)(28,31)(29,33)(30,36)(35,39)(37,38);(8,10)(9,14)(11,18)(12,20)(13,19)(15,21)(16,22)(17,23)(24,26)(25,30)(27,35)(28,36)(29,37)(31,38)(32,34)(33,39);(8,10)(9,15)(11,20)(12,18)(13,19)(14,21)(16,23)(17,22)(25,31)(27,28)(30,38)(32,33)(34,39)(35,36);(8,11,13,12)(9,16,17,21)(10,18,19,20)(14,22,23,15)(24,27,29,28)(25,31,33,32)(26,35,37,36)(30,38,39,34)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11922);