Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18341 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3455 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
898 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,17)(11,15)(12,20)(13,16)(14,18)(19,22)(21,23)(24,25,30,27)(26,33,36,39)(28,32,29,37)(31,38,34,35);(8,10)(9,14)(11,18)(12,21)(13,19)(15,22)(16,23)(17,20)(24,26)(25,31)(27,34)(28,35)(29,38)(30,36)(32,39)(33,37);(8,11,13,12)(9,15,16,20)(10,18,19,21)(14,22,23,17)(24,27,30,25)(26,34,36,31)(28,37,29,32)(33,38,39,35);(9,16)(14,23)(15,20)(17,22)(24,28,30,29)(25,32,27,37)(26,35,36,38)(31,39,34,33)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11329);