Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#34455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| prime radical | C24×C7 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,11,10)(13,17)(14,20)(19,24)(21,26)(28,29)(30,32)(31,35)(33,41)(34,37)(36,42)(38,43)(39,40);(13,17)(18,23)(19,24)(25,27)(28,30,34,31)(29,35,37,32)(33,38,42,39)(36,43,41,40);(8,10,11,9)(12,13)(14,18)(15,19)(16,17)(20,23)(21,25)(22,24)(26,27)(28,31,34,30)(29,35,37,32)(33,39,42,38)(36,43,41,40);(12,14,16,20)(13,18,17,23)(15,21,22,26)(19,25,24,27)(28,32,34,35)(29,30,37,31)(33,40,42,43)(36,38,41,39);(12,15,16,22)(13,19,17,24)(14,21,20,26)(18,25,23,27)(28,33)(29,36)(30,38)(31,39)(32,40)(34,42)(35,43)(37,41)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27443);