Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13442 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2054 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ C7×#405 ◁ G | |
398 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)(9,16)(10,22)(11,27)(12,13)(14,28)(18,31)(19,21)(20,29)(23,32)(24,38)(25,30)(26,36)(33,37)(35,39);(8,9)(10,23)(11,18)(12,19)(13,29)(14,31)(15,21)(16,27)(17,24)(20,28)(22,33)(25,39)(26,35)(30,34)(32,38)(36,37);(8,10,11,24,28,38,12,22,15,26,13,30,14,25,27,36)(9,17,16,23,31,37,29,39,21,34,19,35,20,33,18,32)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6430);