Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23903 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23905 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C7×#3485 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1744 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)(12,13,17,21)(14,18,24,31)(15,19,26,33)(16,27,28,20)(22,34,36,29)(23,37,38,30)(25,32,39,40)(35,42,43,41);(8,9)(10,11)(12,14,17,24)(13,18,21,31)(15,22,26,36)(16,23,28,38)(19,29,33,34)(20,30,27,37)(25,35,39,43)(32,41,40,42);(9,11)(12,15)(13,19)(14,22)(16,25)(17,26)(18,29)(20,32)(21,33)(23,35)(24,36)(27,40)(28,39)(30,41)(31,34)(37,42)(38,43);(12,16)(13,20)(14,23)(15,25)(17,28)(18,30)(19,32)(21,27)(22,35)(24,38)(26,39)(29,41)(31,37)(33,40)(34,42)(36,43)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16893);