Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#20886 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C22×C7×M16 ◁ G | |
1326 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)(12,13,17,22,18,21,16,30)(14,23,26,19,25,34,31,35)(15,27,28,20,29,37,32,36)(24,33,41,42,39,43,40,38);(9,11)(12,14,17,26,18,25,16,31)(13,19,22,34,21,35,30,23)(15,24,28,41,29,39,32,40)(20,33,37,42,36,43,27,38);(12,15)(13,20)(14,24)(16,32)(17,28)(18,29)(19,33)(21,36)(22,37)(23,38)(25,39)(26,41)(27,30)(31,40)(34,42)(35,43);(13,21)(14,25)(20,36)(22,30)(24,39)(26,31)(27,37)(40,41)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13874);