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×#24927 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
862 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)(10,12)(11,13)(14,15)(16,17)(18,23)(19,31)(20,22)(21,26)(24,32)(25,35)(27,38)(28,43)(29,36)(30,39)(33,40)(34,41)(37,42)(44,46)(45,47);(8,10,11,14)(9,12,13,15)(17,22)(18,27)(20,35)(24,31)(25,26)(28,42)(29,30)(32,33)(36,38)(40,41)(43,46)(44,45);(9,13)(12,15)(16,18,21,30)(17,23,26,39)(19,28,34,44)(20,29,35,27)(22,36,25,38)(24,37,40,47)(31,43,41,46)(32,42,33,45);(16,19)(17,24)(18,28)(20,33)(21,34)(22,31)(23,37)(25,41)(26,40)(27,42)(29,45)(30,44)(32,35)(36,43)(38,46)(39,47)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17915);