Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C214 |
| direct product | C7×#62859 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
10986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 43 points:
(1,2,3,4,5,6,7)(9,11)(13,19)(14,20)(17,31)(21,28)(23,33)(26,39)(29,41)(38,43);(8,9)(10,11)(12,13,18,19)(14,15,20,27)(16,28,30,21)(17,22,31,32)(23,36,33,25)(24,26,34,39)(29,40,41,35)(37,43,42,38);(12,14)(13,15)(16,23)(17,24)(18,20)(19,27)(21,25)(22,26)(28,36)(29,37)(30,33)(31,34)(32,39)(35,38)(40,43)(41,42);(12,15)(13,20)(14,19)(16,25)(17,26)(18,27)(21,33)(22,34)(23,28)(24,32)(29,38)(30,36)(31,39)(35,42)(37,40)(41,43);(12,16,18,30)(13,21,19,28)(14,23,20,33)(15,25,27,36)(17,29,31,41)(22,35,32,40)(24,37,34,42)(26,38,39,43);(12,17)(13,22)(14,24)(15,26)(16,29)(18,31)(19,32)(20,34)(21,35)(23,37)(25,38)(27,39)(28,40)(30,41)(33,42)(36,43)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55847);