Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5×C11 · Schur multiplier (H2) = C22 |
| direct product | C5×C11×AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5×C11 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C23×C5×C11 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5×C11 ◁ C2×C4×C5×C11 ◁ G | |
136 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 440 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(17,18)(19,21)(20,22)(23,24);(18,21)(19,24)(22,23);(18,22)(21,23)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1084);