Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#21477 |
| subgroup | G/H | |
|---|---|---|
| center | C7×C8 | #120 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C4×#120 |
| prime radical | C7×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C7×C8 ◁ C22×C7×C8 ◁ G | |
1290 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)(8,9,15,18,14,19,13,29)(10,20,23,16,24,33,30,34)(11,25,26,28,27,17,31,12)(21,35,37,32,38,22,36,39);(8,10)(9,16)(11,21)(12,22)(13,30)(14,24)(15,23)(17,32)(18,33)(19,34)(20,29)(25,39)(26,37)(27,38)(28,35)(31,36);(8,11)(9,17)(10,21)(12,18)(13,31)(14,27)(15,26)(16,32)(19,25)(20,35)(22,33)(23,37)(24,38)(28,29)(30,36)(34,39);(8,12,15,25,14,28,13,17)(9,11,18,26,19,27,29,31)(10,22,23,39,24,35,30,32)(16,21,33,37,34,38,20,36)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14465);