Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24319 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C23×C7 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
930 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)(8,9,12,15)(10,14,11,13)(16,17)(18,22)(19,29)(20,32)(21,25)(23,31)(24,35)(26,43)(27,41)(28,38)(30,42)(33,37)(34,40)(36,45)(39,46)(44,47);(8,10,12,11)(9,13,15,14)(16,18,21,28)(17,22,25,38)(19,26,30,44)(20,33,35,27)(23,39,40,36)(24,41,32,37)(29,43,42,47)(31,46,34,45);(16,19,21,30)(17,23,25,40)(18,26,28,44)(20,34,35,31)(22,36,38,39)(24,42,32,29)(27,46,33,45)(37,47,41,43);(8,11,12,10)(9,14,15,13)(19,30)(23,40)(26,44)(29,42)(31,34)(36,39)(43,47)(45,46)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17307);