Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C2×C7×#2860 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C23×C7×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
2838 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2)(23,24,25,26,27,28,29);(4,6)(8,9)(12,13)(17,20)(18,22);(7,8,11,9)(10,12,14,13)(15,16,19,21)(17,18,20,22);(3,4,5,6)(7,9,11,8)(10,13,14,12)(15,17,19,20)(16,18,21,22);(7,10,11,14)(8,12,9,13)(15,18)(16,20)(17,21)(19,22)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29617);