Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13374 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2023 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ C7×#405 ◁ G | |
360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18,20,35)(11,23)(12,27)(13,16)(14,21,19,37)(15,25)(17,29)(22,31,28,36)(24,33,39,30)(26,34)(32,38);(8,9)(10,19,20,14)(11,15)(12,17)(13,16)(18,21,35,37)(22,33,28,30)(23,25)(24,36,39,31)(26,32)(27,29)(34,38);(8,10)(9,14)(11,24)(12,28)(13,20)(15,31)(16,19)(17,33)(18,34)(21,38)(22,29)(23,35)(25,37)(26,39)(27,30)(32,36)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6362);