Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60367 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C210 |
| direct product | C7×#60370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C2×C7×#585 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C7×#41 ◁ G | |
4746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,18,23)(14,24,27,37)(15,20,28,34)(16,22,17,21)(19,31,33,26)(25,38,39,43)(29,36,30,35)(32,41,42,40);(12,14)(13,19)(15,25)(16,26)(17,31)(18,27)(20,32)(21,24)(22,37)(23,33)(28,39)(29,40)(30,41)(34,42)(35,38)(36,43);(9,11)(12,15)(13,20)(14,25)(16,29)(17,30)(18,28)(19,32)(21,35)(22,36)(23,34)(24,38)(26,40)(27,39)(31,41)(33,42)(37,43);(15,28)(20,34)(25,39)(29,30)(32,42)(35,36)(38,43)(40,41);(12,16,18,17)(13,21,23,22)(14,26,27,31)(15,29,28,30)(19,24,33,37)(20,35,34,36)(25,40,39,41)(32,38,42,43)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53358);