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×#22691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
846 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)(14,26)(15,30)(16,22)(17,24)(18,23)(19,25)(20,28)(21,27)(29,42)(31,39)(32,40)(33,38)(34,43)(35,37)(36,41);(12,14)(13,20)(15,16)(17,31)(18,28)(19,29)(21,37)(22,40)(23,42)(24,26)(25,39)(27,34)(30,43)(32,36)(33,35)(38,41);(12,15,17,32,19,33,18,27)(13,21,23,38,25,40,24,30)(14,16,31,36,29,35,28,34)(20,37,42,41,39,22,26,43);(12,16)(13,22)(14,27)(15,31)(17,36)(18,34)(19,35)(20,38)(21,26)(23,43)(24,41)(25,37)(28,33)(29,32)(30,39)(40,42)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15679);