Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23981 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#2407 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G | |
1300 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)(8,9)(10,11)(12,13)(14,18)(15,17)(16,19)(20,21,23,26)(22,30,32,35)(24,29,25,28)(27,31,34,33);(12,14,15,19)(13,16,17,18)(21,26)(22,31)(24,25)(27,30)(32,33)(34,35);(9,11)(20,22)(21,27)(23,32)(24,31)(25,33)(26,34)(28,35)(29,30);(13,17)(16,18)(21,26)(22,32)(28,29)(31,33)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16969);