Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C8 · Schur multiplier (H2) = C23 |
| direct product | C7×#12792 |
| subgroup | G/H | |
|---|---|---|
| center | C7×C8 | #121 |
| commutator | C2×C4 | C22×C7×C8 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| socle | C2×C7 | #1797 |
| prime radical | C2×C7×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C7×C8 ◁ C22×C7×C8 ◁ G | |
440 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)(8,9,13,20,14,18,25,33,15,21,24,16,12,19,10,22)(11,26,29,38,28,35,23,37,30,36,31,39,27,17,34,32);(8,10,12,24,15,25,14,13)(9,16,18,22,21,20,19,33)(11,23,27,29,30,34,28,31)(17,32,26,38,35,37,36,39);(8,11)(9,17)(10,23)(12,27)(13,31)(14,28)(15,30)(16,32)(18,26)(19,36)(20,37)(21,35)(22,38)(24,29)(25,34)(33,39)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 5780);