Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C2×C7×#1482 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C2×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C42 | C24×C7 |
| socle | C23×C7 | C2×C22⋊C4 |
| prime radical | C2×C7×#121 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ C22×C42×C7 ◁ G | |
1042 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2)(35,36,37,38,39,40,41);(3,4)(5,12)(6,10)(7,15)(8,11)(9,13)(14,17)(16,18)(19,20,22,25,23,26,29,32)(21,24,28,31,27,30,33,34);(3,5)(4,9)(6,13)(7,16)(8,14)(10,17)(11,18)(12,15)(19,21)(20,24)(22,28)(23,27)(25,31)(26,30)(29,33)(32,34);(3,6,8,7)(4,10,11,15)(5,13,14,16)(9,17,18,12)(21,27)(24,30)(28,33)(31,34)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 10445);