Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24775 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
850 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)(9,10)(12,13,17,22,16,21,18,23)(14,24,27,39,26,19,33,35)(15,28,31,37,30,38,32,20)(25,41,29,34,42,36,43,40);(8,9,11,10)(12,14,16,26)(13,19,21,24)(15,29,30,43)(17,27,18,33)(20,36,37,41)(22,35,23,39)(25,31,42,32)(28,40,38,34);(12,15,16,30)(13,20,21,37)(14,25,26,42)(17,32,18,31)(19,34,24,40)(22,38,23,28)(27,43,33,29)(35,41,39,36);(8,10,11,9)(13,21)(19,24)(20,37)(22,23)(28,38)(34,40)(35,39)(36,41)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17763);