Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#33863 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C7×#3280 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×D4 ◁ C7×C8×D4 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,13)(10,14,15,12)(16,17)(18,22)(19,23)(20,33)(21,26)(24,30)(25,31)(27,34)(28,43)(29,37)(32,39)(35,40)(36,41)(38,44)(42,46)(45,47);(8,10)(9,12)(11,15)(13,14)(16,18,21,29)(17,22,26,37)(19,27,32,42)(20,28,31,41)(23,34,39,46)(24,35,38,45)(25,36,33,43)(30,40,44,47);(17,23)(19,30)(20,31)(22,34)(24,25)(26,39)(27,40)(28,41)(32,44)(33,38)(35,36)(37,46)(42,47)(43,45);(10,15)(12,14)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26851);