Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
980 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)(12,13,18,22,19,24,17,23)(14,25,27,20,15,29,28,36)(16,31,32,21,34,38,33,39)(26,35,42,43,30,37,41,40);(8,9)(10,11)(12,14,18,27,19,15,17,28)(13,20,22,29,24,36,23,25)(16,30,32,41,34,26,33,42)(21,37,38,40,39,35,31,43);(9,11)(12,15,19,14)(13,20,24,36)(16,30,34,26)(17,28,18,27)(21,35,39,37)(22,25,23,29)(31,43,38,40)(32,42,33,41);(12,16)(13,21)(14,26)(15,30)(17,33)(18,32)(19,34)(20,35)(22,38)(23,31)(24,39)(25,40)(27,42)(28,41)(29,43)(36,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18182);