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×#24772 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
840 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(9,10)(12,13,16,21,18,23,17,22)(14,19,25,34,26,35,32,39)(15,27,29,38,31,37,30,20)(24,36,28,42,40,43,41,33);(8,9,11,10)(12,14)(13,19)(15,28)(16,25)(17,32)(18,26)(20,36)(21,34)(22,39)(23,35)(24,30)(27,42)(29,40)(31,41)(33,37)(38,43);(12,15,18,31)(13,20,23,38)(14,24,26,40)(16,30,17,29)(19,33,35,42)(21,37,22,27)(25,41,32,28)(34,43,39,36);(8,10,11,9)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17760);