Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#22896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×H(5,𝔽2) | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
1016 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13)(14,25)(15,21)(16,23)(17,22)(18,24)(19,28)(20,30)(26,34)(27,41)(29,40)(31,39)(32,36)(33,37)(35,43)(38,42);(8,10,11,9)(12,14)(13,19)(15,26)(16,32)(17,28)(18,29)(20,34)(21,38)(22,40)(23,25)(24,36)(27,30)(31,43)(33,42)(35,37)(39,41);(12,15,18,31)(13,20,24,37)(14,26,29,43)(16,30,17,33)(19,34,36,35)(21,23,39,22)(25,41,40,38)(27,28,42,32);(12,15)(13,21)(14,27)(16,33)(17,30)(18,31)(19,35)(20,22)(23,37)(24,39)(25,41)(26,32)(28,43)(29,42)(34,36)(38,40)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15884);