Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61486 |
| 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 ◁ C7×#529 ◁ G | |
1794 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)(9,12)(13,15)(16,17)(18,27)(19,31)(20,25)(21,26)(22,35)(23,30)(24,32)(28,43)(29,39)(33,40)(34,38)(36,41)(37,44)(42,46)(45,47);(8,9)(10,13)(11,12)(14,15)(16,18)(17,23)(19,28)(20,34)(21,30)(22,29)(24,37)(25,39)(26,27)(31,47)(32,46)(33,45)(35,38)(36,44)(40,43)(41,42);(16,19)(17,24)(18,28)(20,32)(21,33)(22,36)(23,37)(25,40)(26,41)(27,42)(29,44)(30,45)(31,35)(34,46)(38,47)(39,43);(9,12)(13,15)(16,20,21,22)(17,25,26,35)(18,29,30,34)(19,32,33,36)(23,38,27,39)(24,40,41,31)(28,44,45,46)(37,47,42,43);(8,10,11,14)(9,13,12,15)(18,30)(23,27)(28,45)(29,34)(37,42)(38,39)(43,47)(44,46)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54474);