Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18746 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18795 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
956 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,17)(11,15)(12,20)(13,16)(14,18)(19,22)(21,23)(24,25)(26,34)(27,33)(28,31)(29,32)(30,35)(36,39)(37,38);(8,10,13,19)(9,14,16,23)(11,18,12,21)(15,22,20,17)(24,26,29,37)(25,30,32,39)(27,36,28,35)(31,38,33,34);(25,31)(27,28)(30,38)(32,33)(34,39)(35,36);(8,11,13,12)(9,15,16,20)(10,18,19,21)(14,22,23,17)(25,32)(30,39)(31,33)(34,38)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11783);