Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C2×C7×#3555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
6446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 6 generators on 41 points:
(1,2)(35,36,37,38,39,40,41);(3,4,8,11)(5,6,13,9)(7,15,16,10)(12,17,18,14)(19,20,23,26)(21,24,29,27)(22,30,31,25)(28,33,34,32);(3,5,8,13)(4,9,11,6)(7,12,16,18)(10,17,15,14)(19,20)(21,27)(22,25)(23,26)(24,29)(28,33)(30,31)(32,34);(3,6,8,9)(4,5,11,13)(7,14,16,17)(10,12,15,18);(3,5)(4,9)(6,11)(7,12)(8,13)(10,17)(14,15)(16,18)(19,21)(20,24)(22,28)(23,29)(25,32)(26,27)(30,33)(31,34);(3,7,8,16)(4,10,11,15)(5,12,13,18)(6,14,9,17)(19,22,23,31)(20,25,26,30)(21,28,29,34)(24,32,27,33)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55739);