Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10549 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#10555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #124 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
364 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,12,10)(11,13,15,14)(16,17)(18,22)(19,21)(20,24)(23,27)(25,28)(26,29)(30,31);(8,10,12,9)(11,14,15,13)(17,21)(18,25)(19,27)(22,29)(23,24)(26,31);(9,13)(10,14)(11,15)(16,18,19,25,20,26,27,31)(17,22,23,30,24,29,21,28)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3543);