Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1078 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)(8,9,13,18)(10,20,23,29)(11,16,12,26)(14,19,24,17)(15,27,32,21)(22,36,37,35)(25,34,28,33)(30,38,31,39);(8,10)(9,15)(11,21)(12,27)(13,23)(14,22)(16,29)(17,30)(18,32)(19,31)(20,26)(24,37)(25,38)(28,39)(33,36)(34,35);(8,11,24,28)(9,16,17,33)(10,21,37,39)(12,14,25,13)(15,29,30,36)(18,26,19,34)(20,31,35,32)(22,38,23,27);(9,17)(15,30)(16,33)(18,19)(20,35)(26,34)(29,36)(31,32)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11317);