Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18132 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18138 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C25×C7 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1054 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)(8,9,13,17)(10,18,20,34)(11,22,24,36)(12,15,26,30)(14,27,29,19)(16,31,33,25)(21,32,35,39)(23,28,37,38);(8,10,12,21)(9,14,15,28)(11,23,25,19)(13,20,26,35)(16,32,22,18)(17,29,30,38)(24,37,31,27)(33,39,36,34);(11,24)(16,33)(18,34)(19,27)(22,36)(23,37)(25,31)(32,39);(9,15)(14,28)(16,22)(17,30)(18,32)(29,38)(33,36)(34,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11126);