Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#12820 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #459 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×C8 ◁ G | |
414 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)(14,22)(15,27)(16,31)(17,33)(18,23)(19,25)(20,24)(21,32)(26,40)(28,39)(29,43)(30,35)(34,36)(37,41)(38,42);(12,14,16,25,18,26,32,17)(13,19,21,22,23,33,31,40)(15,24,28,41,30,42,29,34)(20,35,36,39,38,27,37,43);(12,15)(13,20)(14,24)(16,28)(17,34)(18,30)(19,35)(21,36)(22,39)(23,38)(25,41)(26,42)(27,33)(29,32)(31,37)(40,43)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 5808);