Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#29427 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
724 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)(10,14)(11,12)(13,15)(16,17)(18,22)(19,21)(20,23)(24,25,30,34)(26,31,27,36)(28,33,29,38)(32,35,39,37);(9,12)(13,14)(16,18)(17,20)(19,23)(21,22)(24,26,30,27)(25,31,34,36)(28,37,29,35)(32,38,39,33);(18,23)(20,22)(24,27,30,26)(25,32,34,39)(28,37,29,35)(31,38,36,33);(8,10,11,15)(9,13,12,14)(17,21)(20,22)(24,28,30,29)(25,33,34,38)(26,35,27,37)(31,39,36,32)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 22415);