Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#26154 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×D4 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G | |
846 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)(20,21,23,26)(22,28,30,25)(24,27,31,34)(29,35,32,33);(9,11)(12,14,16,15)(13,17,18,19)(22,29)(24,31)(25,33)(27,34)(28,35)(30,32);(12,15,16,14)(13,17,18,19)(20,22,23,30)(21,25,26,28)(24,32,31,29)(27,35,34,33);(9,11)(22,30)(25,28)(29,32)(33,35)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 19142);