Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C5×#1438 ⋊ C2 |
| Sylow | C5 ⋊ #15947 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D5 |
| commutator, socle, cosocle | C24×C5 | C24 |
| Fitting | C5×#1438 | C2 |
| hypercenter | #1438 | D5 |
| hypocenter | C5 | #15947 |
| LCS | G ▷ C24×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ #1438 | |
6146 conjugacy classes of subgroups; only the 363 normal subgroups are shown.
This group has 6146 conjugacy classes of subgroups — too many to draw. Only its 363 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,d^b=de,i^d=i^4146 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#15947, #72242895, #72242897, … |
| maximal normal subgroup of | D5×#15947, #72242895, #72242897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 117080);