Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#20768 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C22×C4⋊C4 |
| prime radical | C24×C7 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C7×#117 ◁ G | |
778 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,21,25,22,26,20,36)(18,27,31,38,29,41,30,23)(19,32,34,39,35,46,33,24)(28,42,45,47,43,37,44,40);(9,12)(13,15)(16,18,20,30,22,29,21,31)(17,23,25,27,26,38,36,41)(19,28,33,44,35,43,34,45)(24,37,32,40,39,42,46,47);(8,10,11,14)(9,13,12,15)(16,19,20,33,22,35,21,34)(17,24,25,32,26,39,36,46)(18,28,30,44,29,43,31,45)(23,37,27,40,38,42,41,47);(18,29)(23,38)(27,41)(28,43)(30,31)(37,42)(40,47)(44,45)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13756);