Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7×C8 · Schur multiplier (H2) = C26 |
| direct product | C7×#17352 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×C22⋊C4 |
| commutator | C22 | C23×C7×C8 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C4×C7×Q8 ◁ G | |
1162 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,10,12,11,13,14,15)(16,17)(18,26,29,22)(19,23)(20,24)(21,25)(27,40,43,34)(28,41,45,35)(30,36)(31,37)(32,38)(33,39)(42,47,44,46);(16,18)(17,22)(19,27)(20,28)(21,29)(23,34)(24,35)(25,26)(30,42)(31,43)(32,44)(33,45)(36,46)(37,40)(38,47)(39,41);(16,19,21,31)(17,23,25,37)(18,27,29,43)(20,32,33,30)(22,34,26,40)(24,38,39,36)(28,44,45,42)(35,47,41,46);(16,20,21,33)(17,24,25,39)(18,28,29,45)(19,30,31,32)(22,35,26,41)(23,36,37,38)(27,42,43,44)(34,46,40,47)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 10340);