Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24468 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24470 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3489 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1360 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)(12,13,18,23,19,24,17,33)(14,25,16,20,27,22,32,36)(15,28,30,39,31,38,34,21)(26,41,42,37,43,35,29,40);(8,9)(10,11)(12,14)(13,20)(15,26)(16,18)(17,32)(19,27)(21,35)(22,23)(24,36)(25,33)(28,40)(29,34)(30,42)(31,43)(37,38)(39,41);(9,11)(12,15,19,31)(13,21,24,39)(14,26,27,43)(16,29,32,42)(17,30,18,34)(20,35,36,41)(22,37,25,40)(23,38,33,28);(12,16)(13,22)(14,17)(15,29)(18,27)(19,32)(20,33)(21,37)(23,36)(24,25)(26,30)(28,35)(31,42)(34,43)(38,41)(39,40)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17458);