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×#34375 |
| 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 | |
1898 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)(12,13,17,15)(14,18,22,20)(16,23,24,19)(21,26,27,25)(29,33)(30,36)(31,39)(41,43);(13,15)(18,20)(19,23)(25,26)(28,29,32,33)(30,37,36,34)(31,35,39,40)(38,43,42,41);(12,14,17,22)(13,18,15,20)(16,21,24,27)(19,25,23,26)(28,29)(30,34)(31,35)(32,33)(36,37)(38,41)(39,40)(42,43);(12,15,17,13)(14,20,22,18)(16,23,24,19)(21,26,27,25)(28,30,32,36)(29,34,33,37)(31,38,39,42)(35,41,40,43);(12,16,17,24)(13,19,15,23)(14,21,22,27)(18,25,20,26)(28,31,32,39)(29,35,33,40)(30,38,36,42)(34,41,37,43)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27363);