Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#23603 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
970 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)(12,13,18,21,17,22,16,30)(14,23,32,34,25,40,26,19)(15,20,31,36,29,37,28,38)(24,39,42,33,41,35,27,43);(8,9)(10,11)(12,14,16,26,17,25,18,32)(13,19,21,23,22,34,30,40)(15,27,28,41,29,42,31,24)(20,35,36,43,37,39,38,33);(9,11)(12,15,17,29)(13,20,22,37)(14,24,25,41)(16,31,18,28)(19,33,34,43)(21,38,30,36)(23,39,40,35)(26,42,32,27);(14,25)(19,34)(23,40)(24,41)(26,32)(27,42)(33,43)(35,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16591);