Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13385 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3061 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(9,10)(12,13)(14,24)(15,20)(16,19)(17,22)(18,26)(21,31)(23,30)(25,33)(27,41)(28,37)(29,35)(32,42)(34,40)(36,43)(38,39);(8,9)(10,11)(12,14)(13,18)(15,26)(16,27)(17,25)(19,34)(20,24)(21,32)(22,37)(23,33)(28,30)(29,40)(31,39)(35,41)(36,38)(42,43);(8,10,11,9)(13,19)(14,25)(16,31)(17,30)(18,32)(20,35)(21,23)(22,36)(24,38)(26,28)(27,40)(29,43)(33,41)(34,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6373);