Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#21558 |
| subgroup | G/H | |
|---|---|---|
| center | C7×C8 | #121 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C4×#121 |
| prime radical | C7×#3067 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C7×C8 ◁ C22×C7×C8 ◁ G | |
876 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,14,19,15,20,13,30)(10,21,12,18,24,35,23,16)(11,25,28,17,29,33,27,34)(22,31,26,36,38,32,37,39);(8,10,13,23,15,24,14,12)(9,16,19,21,20,18,30,35)(11,22,27,37,29,38,28,26)(17,31,33,36,34,32,25,39);(8,11)(9,17)(10,22)(12,26)(13,27)(14,28)(15,29)(16,31)(18,32)(19,33)(20,34)(21,36)(23,37)(24,38)(25,30)(35,39);(8,12,14,24,15,23,13,10)(9,18,19,35,20,16,30,21)(11,26,28,38,29,37,27,22)(17,32,33,39,34,31,25,36)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14546);