Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23530 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×#121 |
| prime radical | C2×C7×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
1350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13)(14,24)(15,29)(16,21)(17,22)(18,23)(19,27)(20,32)(25,34)(26,36)(28,35)(30,42)(31,38)(33,37)(39,40)(41,43);(12,14)(13,19)(15,30)(16,26)(17,27)(18,28)(20,34)(21,24)(22,35)(23,36)(25,33)(29,39)(31,41)(32,40)(37,43)(38,42);(9,11)(12,15,16,31,18,33,17,32)(13,20,22,37,23,38,21,29)(14,25,27,41,28,30,26,40)(19,34,24,39,36,42,35,43);(12,16,18,17)(13,21,23,22)(14,26,28,27)(15,31,33,32)(19,24,36,35)(20,29,38,37)(25,40,30,41)(34,39,42,43)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16518);