Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25183 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×H(5,𝔽2) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
1000 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)(8,9,11,10)(12,13,18,24)(14,25,29,40)(15,31,16,21)(17,35,19,23)(20,30,37,28)(22,33,39,34)(26,38,42,41)(27,36,32,43);(8,10,11,9)(12,14,18,29)(13,20,24,37)(15,32,16,27)(17,30,19,28)(21,38,31,41)(22,36,39,43)(23,40,35,25)(26,34,42,33);(9,10)(12,15,18,16)(13,21,24,31)(14,26,29,42)(17,33,19,34)(20,36,37,43)(22,23,39,35)(25,41,40,38)(27,28,32,30);(12,16,18,15)(13,22,24,39)(14,27,29,32)(17,33,19,34)(20,36,37,43)(21,23,31,35)(25,38,40,41)(26,28,42,30)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18171);