Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18974 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3546 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
930 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)(10,15)(11,16)(12,21)(13,17)(14,18)(19,22)(20,23)(24,25,29,32)(26,34,35,38)(27,30,28,33)(31,36,39,37);(8,10)(9,14)(11,18)(12,20)(13,19)(15,21)(16,22)(17,23)(25,30)(27,28)(31,38)(32,33)(34,39)(36,37);(8,10)(9,15)(11,20)(12,18)(13,19)(14,21)(16,23)(17,22)(24,26)(25,31)(27,37)(28,36)(29,35)(30,38)(32,39)(33,34);(8,11,13,12)(9,16,17,21)(10,18,19,20)(14,22,23,15)(25,32)(26,35)(30,33)(36,37)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11962);