Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24000 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3019 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,21)(12,25)(13,17)(15,24)(16,27)(18,33)(19,35)(20,30)(22,38)(23,32)(26,31)(28,34)(29,37)(36,39);(8,10,13,20)(9,14,17,30)(11,22)(12,19,27,37)(15,28)(16,29,25,35)(18,23)(21,33)(24,36)(26,34)(31,39)(32,38);(8,11)(9,15)(10,18)(12,26)(13,23)(14,28)(16,32)(17,31)(19,36)(20,22)(21,25)(24,27)(29,38)(30,39)(33,35)(34,37);(12,27)(16,25)(19,37)(21,32)(24,26)(29,35)(33,38)(34,36)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16988);