Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13389 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13389 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2033 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
402 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)(9,15)(10,19)(11,13)(12,25)(16,31)(17,34)(18,23)(20,38)(21,26)(22,37)(24,27)(28,36)(29,32)(33,35);(8,9)(10,20)(11,23)(12,17)(13,15)(14,18)(16,22)(19,35)(21,29)(24,39)(25,30)(26,38)(27,34)(28,33)(31,36)(32,37);(8,10,11,21,14,22,13,28)(9,16,15,29,18,20,23,33)(12,26,24,19,27,36,25,37)(17,31,30,35,34,38,39,32)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6377);