Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#20884 |
| 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 ◁ C23×C7×C8 ◁ G | |
1342 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)(14,23,25,19,26,35,31,34)(15,27,28,20,29,37,32,36)(24,33,40,43,41,42,39,38);(9,11)(12,14,17,25,18,26,16,31)(13,19,22,35,21,34,30,23)(15,24,28,40,29,41,32,39)(20,33,37,43,36,42,27,38);(12,15)(13,20)(14,24)(16,32)(17,28)(18,29)(19,33)(21,36)(22,37)(23,38)(25,40)(26,41)(27,30)(31,39)(34,42)(35,43);(13,21)(19,34)(20,36)(22,30)(23,35)(27,37)(33,42)(38,43)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13872);