Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24802 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24804 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
858 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)(12,13,19,23,18,25,17,24)(14,22,16,34,28,36,27,20)(15,29,31,21,33,39,32,38)(26,40,41,37,42,35,30,43);(8,9)(10,11)(12,14,17,27,18,28,19,16)(13,20,23,22,25,34,24,36)(15,26,31,41,33,42,32,30)(21,35,29,37,38,40,39,43);(9,11)(12,15)(13,21)(14,26)(16,30)(17,31)(18,33)(19,32)(20,35)(22,37)(23,29)(24,39)(25,38)(27,41)(28,42)(34,40)(36,43);(12,16,19,28,18,27,17,14)(13,22,24,20,25,36,23,34)(15,30,32,42,33,41,31,26)(21,37,39,35,38,43,29,40)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17792);