Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13316 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#13317 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3054 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C22×C7×M16 ◁ G | |
552 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)(14,22)(15,26)(16,31)(17,20)(18,23)(19,30)(21,29)(24,42)(25,39)(27,37)(28,38)(32,35)(33,41)(34,43)(36,40);(12,14,17,25)(13,18,20,33)(15,27,28,43)(16,32,29,24)(19,35,36,42)(21,37,31,34)(22,38,39,26)(23,40,41,30);(9,11)(15,28)(18,33)(19,36)(23,41)(26,38)(27,43)(30,40)(34,37)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6305);