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×#18340 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
876 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)(10,16)(11,19)(12,14)(13,17)(15,21)(18,23)(20,22)(24,25,29,32)(26,33,35,38)(27,31,28,36)(30,37,39,34);(8,10,12,18)(9,13,14,22)(11,20,21,17)(15,23,19,16)(24,26,29,35)(25,30,32,39)(27,34,28,37)(31,38,36,33);(24,25)(26,30)(27,31)(28,36)(29,32)(33,37)(34,38)(35,39);(9,14)(13,22)(15,19)(16,23)(24,27,29,28)(25,31,32,36)(26,34,35,37)(30,38,39,33)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11328);