Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#26137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#2414 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G | |
894 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)(14,17)(15,19)(16,18)(20,21,25,24)(22,26,29,32)(23,27,31,33)(28,34,35,30);(9,11)(12,14,16,15)(13,17,18,19)(20,22)(21,26)(23,30)(24,32)(25,29)(27,28)(31,34)(33,35);(12,15,16,14)(13,17,18,19)(20,23,25,31)(21,27,24,33)(22,28,29,35)(26,34,32,30);(9,11)(20,21,25,24)(22,26,29,32)(23,27,31,33)(28,34,35,30)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 19125);