Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#33411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator | C8 | C23×C4×C7 |
| Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C2×C7×#41 | D4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C7×#41 ◁ C2×C7×#131 ◁ G | |
658 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)(8,9,10,11)(13,18)(15,26)(16,27)(19,28)(20,29)(21,33)(22,32)(24,39)(25,38)(30,31)(34,37)(35,40)(36,43)(41,42);(12,13,19,33,16,21,15,18,17,22,26,31,27,30,28,32)(14,20,34,43,25,36,24,29,23,35,39,42,38,41,37,40);(12,14)(13,20)(15,24)(16,25)(17,23)(18,29)(19,34)(21,36)(22,35)(26,39)(27,38)(28,37)(30,41)(31,42)(32,40)(33,43);(14,23)(20,35)(24,37)(25,38)(29,40)(34,39)(36,41)(42,43)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26399);