Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#33421 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C7×C8 | C24 |
| commutator | C22 | C23×C7×C8 |
| Frattini, cosocle | C2×C8 | C24×C7 |
| socle | C22×C7 | C23×C8 |
| prime radical | C2×C7×#41 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C7×C8 ◁ G | |
582 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,19,24,20,25,29,37,21,23,30,35,31,36,41,45)(18,22,27,33,28,34,40,44,26,32,38,42,39,43,46,47);(9,12)(13,15)(16,18)(17,22)(19,27)(20,28)(21,26)(23,32)(24,33)(25,34)(29,40)(30,38)(31,39)(35,42)(36,43)(37,44)(41,46)(45,47);(8,10,11,14)(9,13,12,15)(17,23)(22,32)(24,35)(25,36)(33,42)(34,43)(37,45)(44,47);(18,26)(22,32)(27,38)(28,39)(33,42)(34,43)(40,46)(44,47)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26409);