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×#13384 |
| 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)(14,18)(15,19)(16,21)(17,23)(20,28)(22,29)(24,37)(25,34)(26,32)(27,33)(30,36)(31,38)(35,41)(39,43)(40,42);(8,9)(10,11)(12,14)(13,18)(15,25)(16,24)(17,27)(19,34)(20,31)(21,37)(22,32)(23,33)(26,29)(28,38)(30,39)(35,42)(36,43)(40,41);(8,10,11,9)(13,19)(14,24)(15,28)(16,29)(18,31)(20,22)(21,35)(23,36)(25,39)(26,27)(30,41)(32,43)(33,42)(34,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6372);