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×#34405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1990 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)(8,9,10,11)(13,17)(14,20)(19,24)(21,26)(28,29)(30,33)(31,36)(32,37)(34,38)(35,40)(39,41)(42,43);(13,17)(18,23)(19,24)(25,27)(29,30)(31,38)(35,37)(39,43);(12,13)(14,18)(15,19)(16,17)(20,23)(21,25)(22,24)(26,27)(28,30,33,29)(31,36,38,34)(32,37,40,35)(39,42,43,41);(12,14,16,20)(13,18,17,23)(15,21,22,26)(19,25,24,27)(28,31)(29,34)(30,36)(32,39)(33,38)(35,41)(37,42)(40,43);(12,15,16,22)(13,19,17,24)(14,21,20,26)(18,25,23,27)(28,32)(29,35)(30,37)(31,39)(33,40)(34,41)(36,42)(38,43)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27393);