Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#13332 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×C8 ◁ G | |
566 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13)(14,24)(15,20)(16,22)(17,33)(18,23)(19,26)(21,30)(25,34)(27,39)(28,41)(29,40)(31,37)(32,38)(35,43)(36,42);(9,11)(12,14,18,28)(13,19,23,36)(15,29,32,43)(16,25,17,27)(20,24,38,41)(21,39,37,34)(22,40,33,35)(26,31,42,30);(13,20)(14,25)(15,30)(16,17)(19,34)(21,22)(23,38)(24,40)(26,42)(27,28)(31,32)(33,37)(35,41)(36,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6320);