Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#13308 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3061 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(12,13,18,24)(14,25,28,41)(15,29,33,40)(16,23,17,22)(19,35,38,26)(20,34,39,27)(21,31,36,32)(30,42,43,37);(8,9)(10,11)(12,14)(13,19)(15,30)(16,27)(17,34)(18,28)(20,36)(21,39)(22,37)(23,42)(24,38)(25,29)(26,32)(31,35)(33,43)(40,41);(9,11)(12,14)(13,20)(15,26)(16,34)(17,27)(18,28)(19,36)(21,38)(22,41)(23,25)(24,39)(29,42)(30,32)(31,43)(33,35)(37,40)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6296);