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×#3556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| prime radical | C24×C7 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
6338 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);(3,4,8,6)(5,11,13,9)(7,14,15,10)(12,16,18,17)(19,20,24,28)(21,26,22,25)(23,31,32,27)(29,33,30,34);(3,5,8,13)(4,9,6,11)(7,12,15,18)(10,16,14,17)(19,20)(21,26)(22,25)(23,27)(24,28)(29,34)(30,33)(31,32);(19,21,24,22)(20,25,28,26)(23,29,32,30)(27,33,31,34);(3,6,8,4)(5,9,13,11)(7,14,15,10)(12,16,18,17)(19,22,24,21)(20,26,28,25)(23,30,32,29)(27,34,31,33);(3,7,8,15)(4,10,6,14)(5,12,13,18)(9,16,11,17)(19,23,24,32)(20,27,28,31)(21,29,22,30)(25,33,26,34)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55748);