Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3536 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,14,11)(10,20,24,34)(12,18,13,26)(15,19,31,27)(16,29,21,22)(17,30,25,28)(23,36,38,32)(33,39,37,35);(8,10,14,24)(9,16,11,21)(12,22,13,29)(15,23,31,38)(17,32,25,36)(18,34,26,20)(19,33,27,37)(28,35,30,39);(8,11,14,9)(10,21,24,16)(12,17,13,25)(15,27,31,19)(18,30,26,28)(20,35,34,39)(22,32,29,36)(23,37,38,33);(8,12,14,13)(9,17,11,25)(10,22,24,29)(15,28,31,30)(16,32,21,36)(18,27,26,19)(20,33,34,37)(23,35,38,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11413);