Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60932 |
| 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 | |
1768 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17)(18,27)(19,31)(20,26)(21,25)(22,36)(23,30)(24,33)(28,44)(29,40)(32,47)(34,43)(35,39)(37,42)(38,45)(41,46);(8,9)(10,13)(11,12)(14,15)(16,18)(17,23)(19,32)(20,35)(21,30)(22,29)(24,41)(25,27)(26,40)(28,34)(31,44)(33,45)(36,39)(37,46)(38,42)(43,47);(9,12)(13,15)(16,19)(17,24)(18,28)(20,33)(21,34)(22,37)(23,38)(25,42)(26,43)(27,41)(29,45)(30,32)(31,36)(35,46)(39,47)(40,44);(8,10,11,14)(9,13,12,15)(17,25)(23,27)(24,42)(26,36)(31,43)(38,41)(39,40)(44,47);(16,20,21,22)(17,26,25,36)(18,29,30,35)(19,33,34,37)(23,39,27,40)(24,43,42,31)(28,45,32,46)(38,47,41,44)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53920);