Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#19722 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,17)(11,15)(12,21)(13,16)(14,19)(18,22)(20,23)(24,25)(26,35)(27,31)(28,33)(29,38)(30,34)(32,36)(37,39);(8,10,11,18,13,20,12,19)(9,14,21,23,16,22,15,17)(24,26,28,37,30,36,29,27)(25,31,38,32,34,39,33,35);(8,9)(10,14)(11,21)(12,15)(13,16)(17,19)(18,23)(20,22)(24,27,29,36,30,37,28,26)(25,32,33,31,34,35,38,39);(8,11,13,12)(9,15,16,21)(10,18,20,19)(14,17,22,23)(24,28,30,29)(25,33,34,38)(26,27,36,37)(31,32,39,35)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12710);