Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#23374 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle, prime radical | C23×C7 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17)(18,21)(19,23)(20,22)(24,25,27,31,28,30,34,37)(26,29,33,36,32,35,38,39);(8,9)(10,15)(11,12)(13,14)(16,18,21,17)(19,23,20,22)(26,32)(29,35)(33,38)(36,39);(9,12)(13,15)(16,19,21,20)(17,22,18,23)(24,26)(25,29)(27,33)(28,32)(30,35)(31,36)(34,38)(37,39);(8,10,11,14)(9,13,12,15)(16,20,21,19)(17,22,18,23)(25,30)(26,32)(31,37)(33,38)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16362);