Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#22892 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×2−1+4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13,19,25)(14,26,15,29)(16,22,34,40)(17,24,18,23)(20,31,21,28)(27,42,30,38)(32,37,43,36)(33,41,35,39);(8,10,11,9)(12,14,19,15)(13,20,25,21)(16,32,34,43)(17,31,18,28)(22,38,40,42)(23,29,24,26)(27,35,30,33)(36,41,37,39);(12,15,19,14)(13,21,25,20)(16,30,34,27)(17,31,18,28)(22,37,40,36)(23,29,24,26)(32,33,43,35)(38,39,42,41);(12,16)(13,22)(14,27)(15,30)(17,35)(18,33)(19,34)(20,36)(21,37)(23,41)(24,39)(25,40)(26,42)(28,43)(29,38)(31,32)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15880);