Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13440 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C22×C7×D8 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C7×#405 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,18,24)(14,25,29,36)(15,19,16,32)(17,34,31,23)(20,26,38,27)(21,33,22,30)(28,35,41,39)(37,43,40,42);(13,19)(14,26)(15,30)(16,33)(17,31)(21,23)(22,34)(24,32)(25,39)(27,29)(28,43)(35,36)(37,40)(41,42);(9,11)(12,14,15,26,31,41,33,43,18,29,16,27,17,28,30,42)(13,20,21,36,34,40,32,39,24,38,22,25,23,37,19,35)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6428);