Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27×C4 |
| direct product | C7×#60823 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
2054 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)(18,28)(19,34)(20,26)(21,27)(22,38)(23,32)(24,35)(25,36)(29,44)(30,40)(31,45)(33,41)(37,43)(39,47)(42,46);(8,10,11,15)(9,12,13,14)(16,18)(17,23)(19,30)(20,31)(21,32)(22,33)(24,42)(25,40)(26,41)(27,28)(29,36)(34,44)(35,47)(37,46)(38,45)(39,43);(10,15)(12,14)(16,19)(17,24)(18,29)(20,35)(21,36)(22,37)(23,39)(25,26)(27,43)(28,42)(30,32)(31,46)(33,47)(34,38)(40,45)(41,44);(9,13)(12,14)(16,19)(17,25)(18,30)(20,37)(21,36)(22,35)(23,40)(24,26)(27,34)(28,44)(29,32)(31,46)(33,47)(38,43)(39,45)(41,42);(16,20,21,22)(17,26,27,38)(18,31,32,33)(19,35,36,37)(23,41,28,45)(24,25,43,34)(29,46,30,47)(39,44,42,40)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53811);