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×#24023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3486 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1214 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)(10,13)(11,12)(14,15)(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);(9,12)(13,15)(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);(8,10,11,14)(9,13,12,15)(16,19)(17,23)(18,26)(20,34)(21,30)(22,36)(24,42)(25,40)(27,46)(28,44)(29,32)(31,35)(33,45)(37,47)(38,39)(41,43);(9,12)(13,15)(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, 17011);