Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24278 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24282 |
| 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 | |
1308 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)(12,13,19,25)(14,26,16,34)(15,30,33,39)(17,24,18,23)(20,29,22,28)(21,35,38,32)(27,37,31,36)(40,42,43,41);(8,9)(10,11)(12,14,18,29,19,16,17,28)(13,20,24,34,25,22,23,26)(15,27,35,42,33,31,32,41)(21,36,39,43,38,37,30,40);(9,11)(12,15)(13,21)(14,27)(16,31)(17,32)(18,35)(19,33)(20,36)(22,37)(23,30)(24,39)(25,38)(26,40)(28,41)(29,42)(34,43);(12,16,18,28,19,14,17,29)(13,22,24,26,25,20,23,34)(15,31,35,41,33,27,32,42)(21,37,39,40,38,36,30,43)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17270);