Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1828 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#20713 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #381 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#381 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
1244 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)(8,9,13,19,14,18,12,17)(10,20,22,33,23,15,28,30)(11,24,27,31,26,16,25,32)(21,29,35,38,36,34,37,39);(8,10)(9,15)(11,21)(12,22)(13,28)(14,23)(16,29)(17,30)(18,20)(19,33)(24,34)(25,35)(26,36)(27,37)(31,38)(32,39);(8,11)(9,16,18,24)(10,21)(12,25)(13,27)(14,26)(15,29,20,34)(17,31,19,32)(22,35)(23,36)(28,37)(30,38,33,39);(8,12,14,13)(9,17,18,19)(10,22,23,28)(11,25,26,27)(15,30,20,33)(16,31,24,32)(21,35,36,37)(29,38,34,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13701);