Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60749 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C22×C7 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C22×C7×#41 ◁ G | |
2166 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17)(18,23)(19,31)(20,25)(21,34)(22,26)(24,32)(27,41)(28,37)(29,38)(30,44)(33,39)(35,40)(36,43)(42,47)(45,46);(8,10)(9,12)(11,15)(13,14)(16,18)(17,23)(19,27)(20,29)(21,30)(22,28)(24,36)(25,38)(26,37)(31,41)(32,43)(33,42)(34,44)(35,45)(39,47)(40,46);(10,15)(12,14)(16,19)(17,24)(18,27)(20,32)(21,35)(22,33)(23,36)(25,39)(26,40)(28,42)(29,43)(30,45)(31,34)(37,46)(38,47)(41,44);(9,13)(12,14)(18,28)(23,37)(27,42)(29,30)(36,46)(38,44)(41,47)(43,45);(16,20,22,21)(17,25,26,34)(18,29,28,30)(19,32,33,35)(23,38,37,44)(24,39,40,31)(27,43,42,45)(36,47,46,41)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53737);