Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C16 · Schur multiplier (H2) = C22 |
| direct product | C7×#13640 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C7×C16 | C23 |
| commutator | C22 | C22×C7×C16 |
| Frattini, cosocle | C2×C16 | C23×C7 |
| socle | C22×C7 | C22×C16 |
| prime radical | C23×C7 | C2×C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C7×C16 ◁ G | |
194 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)(8,9)(10,13)(11,12)(14,15)(16,17,18,23,19,24,26,35,20,25,27,36,29,37,38,45,21,22,28,32,30,33,39,42,31,34,40,43,41,44,46,47);(9,12)(13,15);(8,10,11,14)(9,13,12,15)(17,22)(23,32)(24,33)(25,34)(35,42)(36,43)(37,44)(45,47)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6628);