Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#21550 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C7×#3054 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C7×C8 ◁ G | |
914 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,17,21,18,22,16,32)(14,23,27,33,24,38,26,19)(15,20,30,36,31,37,29,43)(25,39,41,35,28,42,40,34);(12,14,16,26,18,24,17,27)(13,19,21,23,22,33,32,38)(15,28,29,41,31,25,30,40)(20,35,36,42,37,34,43,39);(9,11)(14,24)(19,33)(23,38)(25,28)(26,27)(34,35)(39,42)(40,41);(12,15,17,30,18,31,16,29)(13,20,21,36,22,37,32,43)(14,25,27,41,24,28,26,40)(19,34,23,39,33,35,38,42)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14538);