Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5×C11 · Schur multiplier (H2) = C25 |
| direct product | C5×C11×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5×C11 | C24 |
| commutator, Frattini, cosocle | C2 | C24×C5×C11 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5×C11 ◁ G | |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 440 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(17,18)(19,23)(20,21)(22,24);(18,21)(22,23);(17,18)(19,22)(20,21)(23,24);(17,19)(18,22)(20,24)(21,23)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1268);