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×#25186 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×2−1+4 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
974 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)(12,13,17,22)(14,23,27,19)(15,28,30,37)(16,18,32,21)(20,31,36,29)(24,33,26,35)(25,40,41,43)(34,39,38,42);(8,10,11,9)(13,18)(14,24)(16,32)(20,28)(21,22)(25,39)(26,27)(29,31)(33,35)(36,37)(40,43)(41,42);(9,10)(12,14,17,27)(13,19,22,23)(15,25,30,41)(16,26,32,24)(18,33,21,35)(20,34,36,38)(28,43,37,40)(29,39,31,42);(12,15)(13,20)(14,25)(16,31)(17,30)(18,28)(19,34)(21,37)(22,36)(23,38)(24,39)(26,42)(27,41)(29,32)(33,43)(35,40)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18174);