Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C2×C42 |
| direct product | C7×#7962 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#95 |
| commutator | C2×C4 | C2×C42×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C24×C7 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C42×C7 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,13,14)(10,12,15,11)(16,17)(18,26,29,30)(19,23)(20,24)(21,25)(22,28,31,27);(8,10,12,14,13,15,11,9)(16,18)(17,22,25,31)(19,27)(20,28)(21,29)(23,30,24,26);(8,11,13,12)(9,10,14,15)(16,19,21,20)(17,23,25,24)(18,27,29,28)(22,30,31,26)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 950);