Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23918 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23938 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G | |
1308 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(12,13)(14,18)(15,17)(16,19)(20,21)(22,30)(23,29)(24,26)(25,28)(27,31)(32,35)(33,34);(8,9)(10,11)(12,14,15,19)(13,16,17,18)(21,26)(27,34)(28,29)(30,35);(9,11)(20,22)(21,27)(23,31)(24,32)(25,33)(26,34)(28,30)(29,35);(13,17)(16,18)(20,23,24,25)(21,28,26,29)(22,31,32,33)(27,30,34,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16926);