Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#33583 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(9,11)(12,13,18,23)(14,24,27,41)(15,22,17,20)(16,29,32,37)(19,34,36,26)(21,28,39,31)(25,42,33,38)(30,40,43,35);(8,9,10,11);(12,14)(13,19)(15,25)(16,30)(17,33)(18,27)(20,35)(21,38)(22,40)(23,36)(24,29)(26,31)(28,34)(32,43)(37,41)(39,42);(12,15,18,17)(13,20,23,22)(14,25,27,33)(16,28,32,31)(19,35,36,40)(21,37,39,29)(24,38,41,42)(26,30,34,43)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26571);