Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#11978 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C4×C8 | C23×C7 |
| prime radical | C7×#466 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(9,13)(10,11)(14,15)(16,17,19,25,33,39,46,41,20,23,34,24,21,26,35,43)(18,27,29,44,36,42,32,37,30,45,28,38,31,40,47,22);(8,9)(10,13)(11,15)(12,14)(16,18)(17,22)(19,32)(20,30)(21,36)(23,37)(24,40)(25,42)(26,44)(27,41)(28,35)(29,46)(31,33)(34,47)(38,39)(43,45);(8,10,12,11)(9,13,14,15)(17,23)(22,37)(24,25)(26,39)(27,45)(38,44)(40,42)(41,43)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4966);