Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24461 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
1318 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)(14,23)(15,29)(16,32)(17,21)(18,22)(19,26)(20,30)(24,28)(25,34)(27,35)(31,36)(33,37)(38,40)(39,42)(41,43);(12,14,18,28)(13,19,22,35)(15,25,31,41)(16,27,17,26)(20,34,37,43)(21,24,32,23)(29,38,36,39)(30,42,33,40);(9,11)(12,13)(14,24)(15,20)(16,21)(17,32)(18,22)(19,26)(23,28)(25,39)(27,35)(29,30)(31,37)(33,36)(34,42)(38,41)(40,43);(12,15,18,31)(13,20,22,37)(14,25,28,41)(16,33,17,30)(19,34,35,43)(21,36,32,29)(23,38,24,39)(26,42,27,40)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17449);