Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23440 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1898 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)(16,23)(17,22)(18,21)(19,26)(20,31)(25,40)(27,35)(28,36)(30,37)(32,38)(33,39)(34,42)(41,43);(9,11)(12,14)(13,19)(15,30)(16,27)(17,26)(18,28)(20,37)(21,35)(22,36)(23,24)(25,32)(29,40)(31,42)(33,41)(34,39)(38,43);(12,15,18,33)(13,20,21,38)(14,25,28,42)(16,32,17,31)(19,34,35,40)(22,39,23,29)(24,37,36,43)(26,30,27,41);(13,21)(19,35)(20,38)(22,23)(24,36)(29,39)(34,40)(37,43)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16428);