Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11521 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#12805 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #410 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C2×#41 | C23×C7 |
| socle | C2×C7 | #1799 |
| prime radical | C7×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C2×C7×C8 ◁ C2×C7×#131 ◁ G | |
434 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18)(11,22)(12,25,26,15)(13,17)(14,19)(16,24)(20,34,35,30)(21,31)(23,29,37,36)(27,32,38,39)(28,33);(8,10,11,19,13,21,24,33)(9,14,16,18,17,28,22,31)(12,20,23,32,26,35,37,39)(15,27,29,30,25,38,36,34);(9,15)(14,27)(16,29)(17,25)(18,30)(22,36)(28,38)(31,34)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 5793);