Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C7 · Schur multiplier (H2) = C23×C8 |
| direct product | C2×C7×#1453 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C7 | C23 |
| commutator | C22 | C22×C42×C7 |
| Frattini, cosocle | C42 | C24×C7 |
| socle | C23×C7 | C2×C42 |
| prime radical | C24×C7 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C7 ◁ G | |
866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2)(27,28,29,30,31,32,33);(3,4,6,10,8,9,7,5)(11,12,14,17,15,18,21,24)(13,16,20,23,19,22,25,26);(3,5,7,9,8,10,6,4)(11,13)(12,16)(14,20)(15,19)(17,23)(18,22)(21,25)(24,26);(4,9)(5,10)(13,19)(16,22)(20,25)(23,26)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 10309);