Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C127 ⋊ C2 |
| Sylow | C127 ⋊ #577 |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,127|a^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^126,e^b=ef,d^c=df1093 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30650491, #30650494, #30650503, … |
| maximal normal subgroup of | #30650491, #30650494, #30650503, … |
| maximal quotient of | #30647256, #30647260, #30647323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1360);