Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C2×C7×#1858 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #120 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | #385 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
1310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2)(35,36,37,38,39,40,41);(3,4,8,12,9,13,7,20)(5,14,16,10,17,25,21,24)(6,11,18,27,19,28,22,26)(15,30,33,34,32,29,31,23);(3,5,8,16,9,17,7,21)(4,10,12,25,13,24,20,14)(6,15,18,33,19,32,22,31)(11,23,27,30,28,34,26,29);(3,6)(4,11)(5,15)(7,22)(8,18)(9,19)(10,23)(12,27)(13,28)(14,29)(16,33)(17,32)(20,26)(21,31)(24,34)(25,30)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13847);