Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23520 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×#121 |
| prime radical | C22×C7×#135 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
1350 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)(15,27)(16,21)(17,32)(18,22)(19,25)(20,31)(24,40)(26,35)(28,39)(29,42)(30,38)(33,36)(34,43)(37,41);(12,14)(13,19)(15,28)(16,25)(17,33)(18,26)(20,37)(21,35)(22,36)(23,32)(24,31)(27,34)(29,43)(30,41)(38,39)(40,42);(9,11)(12,15,17,30,18,31,16,29)(13,20,21,38,22,27,32,42)(14,24,25,41,26,28,33,43)(19,34,23,39,36,37,35,40);(12,16,18,17)(13,21,22,32)(14,25,26,33)(15,29,31,30)(19,35,36,23)(20,38,27,42)(24,41,28,43)(34,40,37,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16508);