Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#33708 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C7×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,31)(19,24)(20,26)(21,40)(22,42)(23,30)(25,36)(27,32)(28,41)(29,39)(33,47)(34,43)(35,44)(37,46)(38,45);(9,12)(13,15)(16,18,32,37,20,35,41,38,23,36,22,34,39,33,21,19)(17,24,40,47,29,43,42,25,30,45,28,44,26,46,27,31);(8,10,11,14)(9,13,12,15)(16,19,21,33,39,34,22,36,23,38,41,35,20,37,32,18)(17,25,27,43,26,47,28,24,30,31,42,46,29,44,40,45);(16,20,23,39)(17,26,30,29)(18,33,36,35)(19,34,38,37)(21,32,41,22)(24,43,45,46)(25,44,31,47)(27,28,42,40)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26696);