Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13343 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#13343 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C23×C5 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ G | |
1084 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 1084 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,3,4,5)(6,7)(8,9)(11,14)(15,17);(10,11)(12,14)(13,15)(16,17);(7,9)(12,16)155 conjugacy classes — view the full character table.
| Fitting subgroup of | D5×#13343, AGL(1,𝔽5)×#13343 |
| maximal subgroup of | D5×#13343 |
| maximal normal subgroup of | D5×#13343 |
| maximal quotient of | C5×#144366 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 6331);