Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#10800 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C2×C42 |
| commutator | C2×C4 | C2×C42×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle | C22×C7 | #376 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ G | |
650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13)(14,23,26,37)(15,20)(16,21)(17,31)(18,22)(19,25,33,27)(24,36,39,43)(28,34)(29,41)(30,35)(32,38,42,40);(12,14,17,27,18,26,16,25)(13,19,21,23,22,33,31,37)(15,24,29,40,30,39,28,38)(20,32,34,36,35,42,41,43);(9,11)(12,15,16,28,18,30,17,29)(13,20,21,34,22,35,31,41)(14,24,25,38,26,39,27,40)(19,32,23,36,33,42,37,43)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3788);