Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#11856 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3169 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
378 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,16,18,13)(11,14)(12,15)(17,22,19,21)(20,23)(24,25)(26,29)(27,36)(28,32)(30,33)(31,34)(35,38)(37,39);(8,10)(9,13)(11,19)(12,18)(14,22)(15,16)(17,20)(21,23)(25,29)(26,33)(27,34)(30,31)(32,38)(35,39)(36,37);(8,11,12,20)(9,14,15,23)(10,17,18,19)(13,21,16,22)(24,26,34,39,28,35,27,33)(25,30,36,38,32,37,31,29)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4844);