Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9279 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9292 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
426 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,12,15,13,10,11,14)(16,17)(18,26)(19,30,32,23)(20,33)(21,25)(22,28)(24,35)(27,40,43,47)(29,41)(31,38,34,39)(36,42,46,44)(37,45);(8,10,13,9)(11,14,12,15)(16,18,20,28,21,29,35,45)(17,22,24,26,25,37,33,41)(19,27,34,44,32,43,31,42)(23,36,39,40,30,46,38,47);(8,9,13,10)(11,15,12,14)(16,19)(17,23)(18,27)(20,34)(21,32)(22,36)(24,39)(25,30)(26,40)(28,44)(29,43)(31,35)(33,38)(37,46)(41,47)(42,45)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2280);