Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25182 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#454 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
992 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)(8,9,11,10)(12,13)(14,19)(15,27)(16,18)(17,22)(20,28)(21,31)(23,34)(24,39)(25,32)(26,35)(29,36)(30,37)(33,38)(40,42)(41,43);(8,10,11,9)(13,18)(14,23)(16,31)(20,27)(21,22)(24,38)(25,26)(28,29)(32,34)(36,37)(39,42)(40,41);(9,10)(12,14,17,26)(13,19,22,35)(15,24,30,40)(16,25,31,23)(18,32,21,34)(20,33,36,43)(27,39,37,42)(28,38,29,41);(12,15)(13,20)(14,24)(16,29)(17,30)(18,27)(19,33)(21,37)(22,36)(23,38)(25,41)(26,40)(28,31)(32,39)(34,42)(35,43)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18170);