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×#23045 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
844 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)(12,13,17,22,18,23,16,21)(14,24,27,19,28,34,26,35)(15,20,31,38,32,39,30,37)(25,36,40,33,41,43,29,42);(8,10,11,9)(12,14)(13,19)(15,29)(16,27)(17,26)(18,28)(20,36)(21,34)(22,24)(23,35)(25,30)(31,41)(32,40)(33,37)(38,42)(39,43);(12,14)(13,19)(15,25)(16,26)(17,27)(18,28)(20,33)(21,24)(22,34)(23,35)(29,30)(31,40)(32,41)(36,37)(38,43)(39,42);(12,15,17,31,18,32,16,30)(13,20,22,38,23,39,21,37)(14,25,27,40,28,41,26,29)(19,33,34,43,35,42,24,36)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16033);