Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#22898 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | D42 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | #2358 |
| prime radical | C7×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C4×C7 ◁ G | |
996 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)(8,9,12,18,13,19,28,17)(10,16,22,31,23,30,21,14)(11,24,25,34,27,33,26,15)(20,35,37,39,38,29,36,32);(8,10,12,22,13,23,28,21)(9,14,18,16,19,31,17,30)(11,20,25,37,27,38,26,36)(15,29,24,32,34,35,33,39);(8,11)(9,15)(10,20)(12,25)(13,27)(14,29)(16,32)(17,33)(18,24)(19,34)(21,36)(22,37)(23,38)(26,28)(30,39)(31,35);(8,10)(9,16)(11,20)(12,22)(13,23)(14,17)(15,32)(18,31)(19,30)(21,28)(24,35)(25,37)(26,36)(27,38)(29,33)(34,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15886);