Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#23601 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×#121 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
994 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)(12,13,16,21,18,22,17,31)(14,23,25,34,27,40,26,19)(15,20,32,37,30,38,29,36)(24,39,42,33,41,35,28,43);(8,9)(10,11)(12,14,17,26,18,27,16,25)(13,19,21,23,22,34,31,40)(15,28,29,41,30,42,32,24)(20,35,37,43,38,39,36,33);(9,11)(12,15)(13,20)(14,24)(16,29)(17,32)(18,30)(19,33)(21,36)(22,38)(23,39)(25,28)(26,42)(27,41)(31,37)(34,43)(35,40);(12,16,18,17)(13,21,22,31)(14,25,27,26)(15,29,30,32)(19,23,34,40)(20,36,38,37)(24,28,41,42)(33,39,43,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16589);