Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18232 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3534 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1002 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)(10,14)(11,13)(12,16)(15,19)(17,21)(18,20)(22,23)(24,25,28,31)(26,29,33,36)(27,30,34,37)(32,38,39,35);(9,13)(11,19)(14,20)(15,16)(18,23)(21,22)(24,26)(25,29)(27,32)(28,33)(30,35)(31,36)(34,39)(37,38);(8,10)(9,14)(11,18)(12,17)(13,20)(15,22)(16,21)(19,23)(24,27)(25,30)(26,32)(28,34)(29,35)(31,37)(33,39)(36,38);(10,17)(14,21)(18,23)(20,22)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11220);