Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17367 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#20593 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×2−1+4 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C7×#41 ◁ G | |
3594 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)(8,9)(10,11)(12,13,16,21,17,20,29,34)(14,22,24,35,25,18,28,31)(15,19,27,33,26,32,39,42)(23,36,38,43,37,30,40,41);(12,14,17,25)(13,18,20,22)(15,23,26,37)(16,28,29,24)(19,30,32,36)(21,35,34,31)(27,40,39,38)(33,43,42,41);(9,11)(12,15)(13,19)(14,23)(16,27)(17,26)(18,30)(20,32)(21,33)(22,36)(24,38)(25,37)(28,40)(29,39)(31,41)(34,42)(35,43);(15,26)(19,32)(23,37)(27,39)(30,36)(33,42)(38,40)(41,43)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13581);