Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#21784 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2308 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18,21,14)(11,22,24,34)(12,17)(13,16)(15,23,31,26)(19,35)(20,33,25,29)(27,32)(28,36)(30,38)(37,39);(8,10)(9,14)(11,19)(12,25)(13,21)(15,30)(16,18)(17,33)(20,27)(22,39)(23,38)(24,37)(26,36)(28,31)(29,32)(34,35);(8,11,13,24)(9,15,16,31)(10,19,21,37)(12,26,27,23)(14,28,18,30)(17,34,32,22)(20,38,25,36)(29,35,33,39);(8,10)(9,14)(11,19)(12,20)(13,21)(15,28)(16,18)(17,29)(22,39)(23,36)(24,37)(25,27)(26,38)(30,31)(32,33)(34,35)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14772);