Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#22899 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | D42 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | #2358 |
| prime radical | C7×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C4×C7 ◁ G | |
1016 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3,4,5,6,7)(8,9,13,18,15,19,14,17)(10,20,22,23,12,11,21,16);(8,10,13,22,15,12,14,21)(9,16,18,20,19,23,17,11);(8,11)(9,10)(12,19)(13,16)(14,23)(15,20)(17,21)(18,22);(8,12)(9,11)(10,15)(13,21)(14,22)(16,18)(17,23)(19,20)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15887);