Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#25985 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×2−1+4 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
842 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)(18,28)(19,23)(20,26)(21,27)(22,31)(24,33)(25,37)(29,42)(30,39)(32,40)(34,43)(35,44)(36,41)(38,45)(46,47);(16,18,21,32)(17,22,27,41)(19,30,35,45)(20,36,37,31)(23,42,44,47)(24,39,43,38)(25,40,26,28)(29,33,46,34);(8,10,11,15)(9,12,13,14)(16,19)(17,23)(18,29)(20,33)(21,35)(22,38)(24,26)(25,43)(27,44)(28,42)(30,36)(31,45)(32,46)(34,37)(39,41)(40,47);(16,19)(17,24)(18,30)(20,34)(21,35)(22,39)(23,26)(25,44)(27,43)(28,42)(29,36)(31,46)(32,45)(33,37)(38,41)(40,47)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18973);