Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#22895 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#454 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
1008 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)(8,9,11,10)(12,13,18,23)(14,24,27,40)(15,20,31,39)(16,22,17,21)(19,32,35,26)(25,42,29,36)(28,37,43,34)(30,41,33,38);(8,10,11,9)(12,14)(13,19)(15,28)(16,32)(17,26)(18,27)(20,36)(21,40)(22,24)(23,35)(25,30)(29,33)(31,43)(34,38)(37,41)(39,42);(12,14)(13,19)(15,29)(16,26)(17,32)(18,27)(20,37)(21,24)(22,40)(23,35)(25,31)(28,33)(30,43)(34,39)(36,41)(38,42);(12,15)(13,20)(14,25)(16,33)(17,30)(18,31)(19,34)(21,41)(22,38)(23,39)(24,42)(26,43)(27,29)(28,32)(35,37)(36,40)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15883);